We study the computability properties of symmetric hyperbolic systems of PDE’s (Formula presented.), with the initial condition u|t=0 = φ(x1, . . ., xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A, B1, . . ., Bm satisfying some natural conditions) any initial function φ ∈ Ck+1(Q, ℝn), k ≥ 1, to the unique solution u ∈ Ck(H, ℝn), where Q = [0, 1]m and H is the nonempty domain of correctness of the system.