How can I calculate the elasicity in a rubber rod.

See:

http://en.wikipedia.org/wiki/Torsion_(mechanics)

You can determine the material's shear modulus by clamping one end and applying a torque at the other, and seeing how miuch the rod twists. The basic equation is:


G = \frac {TL} {J \phi}


where:
G = Shear modulus, which is basically the torsional modulus you are looking for,
T = torque applied at one end of the rod,
L = length of the rod,
J = the torsion constant for the rod - for a round or tubular rod this is the same as its polar moment of inertia, and
\phi = angle of deflection, in radians.