In this paper we consider the numerical approximation of the solution of the 2D unsteady Lame equations on a rectangular domain. The basic problems that appear, using both finite difference and finite element methods, are connected with the fact that these equations are strongly coupled. Thus it is natural to design computational algorithms in such a way that they allow one to consider boundary value problems only for uncoupled equations. To implement this general concept, some special (unconditionally stable) operator-splitting schemes are constructed. Its major peculiarity is that transition to the next time level is performed by solving separate elliptic problems for each component of the displacement vector. The previous results make it possible to design efficient numerical algorithms for elasticity equations.