The wave propagation in nonisotropic media can be discribed by the variable coefficiens wave equations, which can account for the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. A lot of work has been done on the periodic solutions of the nonlinear wave equations with variable coefficients. However, there are few researches on periodic solutions of the coupled variable coefficient problems. In this talk, we discuss the linearly coupled wave equation with sub-linear growth nonlinearity and the nonlinearly coupled wave equation with sup-linear growth nonlinearity. We proved that there are infinitely many periodic solutions for the both problems.