  In the present paper we develop the Virtual Element Method for hyperbolic
problems on polygonal meshes, considering the linear wave equations as our
model problem. After presenting the semi-discrete scheme, we derive the
convergence estimates in H^1 semi-norm and L^2 norm. Moreover we develop a
theoretical analysis on the stability for the fully discrete problem by
comparing the Newmark method and the Bathe method. Finally we show the
practical behaviour of the proposed method through a large array of numerical
tests.
