Elastomers (rubber and rubber-like materials) are widely used in machine building, shipbuilding, civil engineering due to their specific properties: high elasticity, resistance to environmental factors, good dynamic behaviour. Rubberware find an application as compensation devices, isolators, bumpers, shock absorbers, dampers and so on. The important parameters of rubber devices are compression, bending and shear stiffness - the dependence between imposed force and received deformation. In this paper rubber blocks of cylindrical forms under static axial compressive load are considered. Rubber cylinders are considered of finite length with a stress-free side surface and the different types of boundary conditions at the ends, that is, with different methods of fixing the end portions: fixed or bonding by gluing, free support with friction, fixed in the cap. For each case the theoretical dependence of the axial displacement on acting forces (compressive stiffness) are derived using the principle of minimum total potential energy with help of Ritz's method. Five samples of cylindrical rubber blocks with different end conditions were manufactured and tested on loading machine HB Zwick Roell Z-150. The results of analytical solutions are compared with experimental data.