The early phase of the hydrodynamic evolution following collision of two stars is analyzed. Two strong shocks propagate at a constant velocity (which is a small fraction of the velocity of the approaching stars) from the contact surface toward the center of each star. The shocked region near the contact surface has a planar symmetry and a uniform pressure. The density vanishes at the (Lagrangian) surface of contact and the speed of sound diverges there. The temperature, however, reaches a finite value, since as the density vanishes, the finite pressure is radiation dominated. For Carbon-Oxygen white dwarfs collisions this temperature is too low for any appreciable nuclear burning at early times. The divergence of the speed of sound limits numerical studies of stellar collisions, as it makes convergence tests exceedingly expensive unless dedicated schemes are used. We provide a new one-dimensional Lagrangian numerical scheme to achieve this. Self-similar planar solutions are derived for zero-impact parameter collisions between two identical stars, under some simplifying assumptions. These solutions provide rough approximations that capture the main features of the flow and allow a general study as well as a detailed numerical verification test problem. The self-similar solution in the upstream frame is the planar version of previous piston problems that were studied in cylindrical and spherical symmetries. We found it timely to present a global picture of self similar piston problems. In particular, we derive new results regarding the non trivial transition to accelerating shocks at sufficiently declining densities (not relevant for collisions).

7 pages, 5 figures (without appendices). Submitted to ApJ