One very accurate method is AFM in contact mode. But I'm not sure whether you can apply this method to your work - from your question I understand you want to use it for screening, is that correct?
This is not exactly my field of expertise but I would say that it depends on what kind of mechanical properties are you looking for. Cell movement can be easily identified by a tracking software on a fluorescent marker. If you're looking for diffusion I would recommend FRAP technics (I've done FRAP before so please ask if you need more information about this one). But if you're looking for properties like stiffness, tension,... I think magnetic tweezers are quite good for this. Look at this two articles:
I've seen a talk given by him in which he was able to distinguish cancerous from healthy cells by measuring their mechanical properties. I think he mainly uses optical tweezers.
If it is a cell suspension you may even use rheology for characterization. It gives you loss module of the suspension and its viscosity at various shear rates/stresses. If you want to try this method, I can help you. Looking at singular cells, I also suggest the use of magnetic tweezers. Micropipette methods have also been used for measurement of erythrocyte wall stiffnes.
my experience is only related to collagenous tissues. As Dr. Joachim summarized there are several equipments and techniques to measure different parameters at different levels.
Talking about tissue... I don't know exactly what are you going to analyze and which parameters you want to compare (viscosity, tensile strength, elasticity, stiffness etc...) and if you need to know exactly the values of these parameters or if you only need to compare the effects of different treatments. If you only need to compare different treatments it could be really easy and rather inexpensive, otherwise you should use specific equipment such as force transducers, DMA (Dynamic mechanical analyzer).
To determine the mechanical properties of cells you have a number of options. The top four methods are,
1) Indentation/Compression (force or displacement sensing)
2) Optically by deforming the cell (pipetting or flow)
3) Rheometry
4) Oscillatory magnetic sphere attached to a cell (Power law structural damping)
There are a number of highly critical reviews on the determination of material parameters for cells and the contact mechanics for dealing rigorously with general tissues and cells is still in its infancy, so be careful! A reasonable review for reporting on techniques and approaches for the determination of material parameters may be found at Journal of Biomechanics Volume 39, Issue 2, 2006, Pages 195–216 (http://www.sciencedirect.com/science/article/pii/S0021929004005949).
Indentation is probably the best approach to date (http://pubs.rsc.org/en/content/articlelanding/2013/sm/c3sm50706h#!divAbstract), as techniques exist at most length and time scales and is very robust. The work of Moeendarbary et al. (http://www.nature.com/nmat/journal/v12/n3/full/nmat3517.html) represents a summary of the most comprehensive indentation experimental study to date and it is a shame that the analysis did not benefit from the insights of the preceding paper, as such treat the theoretical section and some of the interpretations based on them with caution, since the model does not consider the compliant element correctly which is now known to be crucial in the determination of material parameters. If you read the supporting information where the poroelastic model is expanded to a single term, this is equivalent to a single relaxation viscoelastic model and as such cannot be used to unambiguously say a cell is poroelastic. The editorial accompanying the nature issue effectively makes a number of further comments indicating caution in treating a cell as poroelastic.
Optically has some nice features, a solid body does not make contact (except pipetting) but micro-channels can yield an interesting and useful material parameters, see something by C. Pozrikidis (say Modelling and simulation of capsules and biological cells, ISBN: 1-58488-359-6), of limited use for assessment of tissues
Rheometry can produce interesting results for tissues, see a review by C. Verdier (http://www.kurims.kyoto-u.ac.jp/EMIS/journals/HOA/CMMM/Volume5_2/459319.pdf) for more information.
Oscillatory magnetic sphere read Fabry et al. (http://pre.aps.org/abstract/PRE/v68/i4/e041914), there are some interesting results from this approach but I have no experience of it when compared to other approaches. I typically view that this approach probes the interior of the cell more than the other approaches because of how the particles are attached to the cell.
It is rare for two different techniques to agree on material parameters! The exact reason for this is unknown, but so long as the techniques are of the same order it is reasonable to assume that the material properties have been determined well. Tissues are generally easier to characterise than cells and typically have smaller variation from a consistent source than individual cells from a consistent source.
If you are looking to measure tissue properties in vivo, you may want to consider elastography. The general idea is to use an imaging modality to visualize wave propagation through the tissue of interest.
One can also use elastography for mapping subcellular distributions of elastic modulus and stress. See Canovic et al. BMMB 2013 and Lam et al. Integr. Biol. 2012.
I am thinking in different microtubules in the periphery, whose give the diferentiation to the cell.
The periphery give the function to the cell and it's no,t in cancer cell, its development. Cancer cell is split prematurely, before reaching the functional size.
(I'm thinking in the peptids and signal paths whose make its development).