Using holography, we study the collision of planar shock waves in strongly coupled N = 4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.Introduction.-The recognition that the quark-gluon plasma (QGP) produced in relativistic heavy ion collisions is strongly coupled [1], combined with the advent of gauge/gravity duality (or "holography") [2,3], has prompted much work exploring both equilibrium and non-equilibrium properties of strongly coupled N = 4 supersymmetric Yang-Mills theory (SYM), which may be viewed as a theoretically tractable toy model for real QGP. Multiple authors have discussed collisions of infinitely extended planar shock waves in SYM, which may be viewed as instructive caricatures of collisions of large, highly Lorentz-contracted nuclei. In the dual description of strongly coupled (and large N c ) SYM, this becomes a problem of colliding gravitational shock waves in asymptotically anti-de Sitter (AdS 5 ) spacetime. Previous work has examined qualitative properties and trapped surfaces [4][5][6][7], possible early time behavior [8][9][10], and expected late time asymptotics [11,12]. As no analytic solution is known for this gravitational problem, solving the gravitational initial value problem numerically is the only way to obtain quantitative results which properly connect early and late time behavior. In this letter, we report the results of such a calculation, and examine the evolution of the post-collision stress-energy tensor.Unlike previous work considering singular shocks with vanishing thickness [5,9], or shocks driven by nonvanishing sources in the bulk [5,6], we choose to study planar gravitational "shocks" which are regular, nonsingular, source-less solutions to Einstein's equations. Equivalently, we study the evolution of initial states in SYM with finite energy density concentrated on two planar sheets of finite thickness (and Gaussian profile), propagating toward each other at the speed of light. The dual description only involves gravity in asymptotically AdS 5 spacetime; the complementary 5D internal manifold plays no role and may be ignored. Consequently, our results apply to all strongly coupled 4D conformal gauge theories with a pure gravitational dual description.