One of the most widely used methods proposed in [W. Oliver, G. Pharr. J. Mater.Res. 7, 1564 (1992)]. In [D. Joslin, W. Oliver. J. Mater.Res. 5, 123 (1990)], it was proposed to use the ratio of the applied load P to the square of the contact stiffness S^2. However, to obtain correct results it is necessary that the film and the substrate had similar values of elastic modulus and hardness.

In the paper [A.R.Shugurov, A.V.Panin, K.V.Oskomov Specific Features of the Determination of the Mechanical Characteristics of Thin Films by the Nanoindentation Technique // Physics of Solid State 50, No. 6, 1050 (2008)] it is shown that the Oliver-Pharr method in combination with a method of calculating the true film hardness allows one to correctly determine the hardness of

thin films deposited on the substrate, independently of the hardness ratio between the film and substrate. There is also a method of excitation of resonant flexural vibrations in the sample using relationship between the natural frequencies of oscillations and mechanical properties of the system [E.Mfoumou, C.Hedberg, S.Kao-Walter Static versus low frequency dynamic elastic modulus measurement of thin films // Electronic Journal Technical Acoustics 17 (2006), www.ejta.org].

please use google before asking questions in here:

http://www.sciencedirect.com/science/article/pii/S0020768307002533

One of the most widely used methods proposed in [W. Oliver, G. Pharr. J. Mater.Res. 7, 1564 (1992)]. In [D. Joslin, W. Oliver. J. Mater.Res. 5, 123 (1990)], it was proposed to use the ratio of the applied load P to the square of the contact stiffness S^2. However, to obtain correct results it is necessary that the film and the substrate had similar values of elastic modulus and hardness.

In the paper [A.R.Shugurov, A.V.Panin, K.V.Oskomov Specific Features of the Determination of the Mechanical Characteristics of Thin Films by the Nanoindentation Technique // Physics of Solid State 50, No. 6, 1050 (2008)] it is shown that the Oliver-Pharr method in combination with a method of calculating the true film hardness allows one to correctly determine the hardness of

thin films deposited on the substrate, independently of the hardness ratio between the film and substrate. There is also a method of excitation of resonant flexural vibrations in the sample using relationship between the natural frequencies of oscillations and mechanical properties of the system [E.Mfoumou, C.Hedberg, S.Kao-Walter Static versus low frequency dynamic elastic modulus measurement of thin films // Electronic Journal Technical Acoustics 17 (2006), www.ejta.org].

W. Oliver, G. Pharr. J. Mater.Res. 7, 1564 (1992)

if you mean measure, may ne use a DMA

 Check this method proposed by the Emmerich and Luengo (1993: 1995)  called  microscopic cross-linking model based on X-ray diffraction profile data and volume fraction of the sample

Refrencess

Emmerich, F.G. and  Luengo, C.A. 1993. Young’s modulus of heat-treated carbons: a theory for nongraphitizing carbons. Carbon 31(2): 333-339.

Emmerich, F.G. 1995a. Application of a cross-linking model to the Young's       modulus of graphitizable and non-graphitizable carbons. Carbon 33(1): 47-            50.

This has also been a subject of recent work for our group, to address mechanical limitations of our coatings.  See "Nano-indentation of single-layer optical oxide thin films grown by electron-beam deposition"

K. Mehrotra, J. B. Oliver, and J. C. Lambropoulos

Please go through below links. These articles might be helpful. 

http://onlinelibrary.wiley.com/doi/10.1002/app.43532/full

http://www.sciencedirect.com/science/article/pii/S0032386116301227

Best way to measure young's modulus is using High resolution XRD by different geometry method.