If such proportionality exists, I doubt that it is linear and there are exceptions :

Fat is stiffer than blood but has lower density.

A contracted muscle is stiffer than a relaxed one but they have equal density.

The same holds for the wall of a full bladder versus an empty one.

The same holds for a corpse versus a living person.

Blood with contrast agent has very high density.

Additionally to the points that Lambert brought up, HU are based on a very relatively simple calibration method... and the polychromatic nature of the X-Ray source used in clinical/lab-based CT imaging wouldn't allow precise measurements.

Thanks for your answer Lambert and Michael.

Well, I should have squeezed my question first. If one wants to talk about the whole biological tissues generally, you're absolutely right, but I intend to find a correlation between elastic modulus, density and CT number(i.e. HU) of the arterial calcium. As you mentioned HU may not represent geometry, size and type intrinsically and it shows gray level in element. However it seems "statistics" do the thing here. I found the following paper apparently suits what I'm looking for:

Rho, J.Y., Hobatho, M.C., and Ashman, R.B. “Relations of Mechanical Properties to Density and CT Numbers in Human Bone” Medical Engineering and Physics, Vol. 17, No. 5 (1995) 347-355

If you refer to the reference, you'll find more related articles. Here elastic modulus/density and CT number of the cortical and spongy bones are correlated using linear and exponential regression empirically which I found it useful. Likewise, I found another paper which directly converts HU to density for radiotherapy application.

So I guess if I confine my problem to a specific HU with specific xray energy, despite the fact that the equations are obtained experimentally, but I might be able to exploit them hopefully... If you think I'm wrong somewhere please correct me. Thanks.

You are right about the almost linear relationship of density and HUs.

Maybe if you only consider a specific TISSUE, a relationship between stiffness and HUs can be established; the article you referenced is about BONE.

Even in bone the HUs and streghth are not so easy to correlate. A good example can be found in osteoporosis, in osteoporosis the density is low i.e. a lower HU compared to healthy bone. In the day and age when Fluor was considered to be a good therapy for osteoporosis the density of bone did indeed increase however, the bone did become more brittle resulting in fracture risk increase. Finding a good correlation will thus be very difficult.