Rubber's resistance to compression along one axis I'm concerned with application of rubber sealings. I need to find out what Force is needed to compress this  piece of rubber (the rubber cannot move in the z direction, consider the width of rubber there dz=const). A relevant property I've found is the bulk modulus, but it is about a uniform compression. Thanks.

 A: This calculation is not trivial at all, you will need very accurate data, characteristically trickie to measure ecperimentally.
Let us assume in first approximation  that your rubber is incompressible (infinite bulk modulus).
For small deformation, the elastic modulus will allow you to calculate the force you are after.
For larger deformations, like what is expected in a seal, rubber will behave non-linearly, and you need to characterise a suitable material model. You will as a minimum need experimental data in compression, not something you will find on a typical datasheet.
A practical, engineering,  workaround exists, to get an order of magnitude estimate. In a real scenario, friction will prevent the deformation mode you highlight: compressing a seal will reduce the height of it, and friction will prevent lateral contraction. Then, the bulk modulus, that you should find on a datasheet, could be used. Calculate the volumes before and after compression, and use the bulk modulus to estimate the force required for the volune contraction
