Summary: We study the asymptotic behavior of the distributions of solutions of the randomly perturbed wave equations \(\partial^2 u_\varepsilon(t,x)/\partial t^2= a^2 (y(t/\varepsilon))\Delta u_\varepsilon (t,x)\) in a bounded region \(G\) with a smooth boundary \(\Gamma\), with some initial and zero boundary conditions on \(\Gamma\), where \(y(t)\) is an ergodic jump Markov process. It is shown that the distributions of the random field \(u_\varepsilon(t/\varepsilon,x)\) coincide asymptotically with the distribution of a random field which is represented by its series expansion in terms of the eigenfunctions of the Laplace operator \(\Delta\) in the region \(G\) with zero boundary condition on \(\Gamma\) with coefficients depending on a sequence of independent Wiener processes.