Abstract: As is known, some engineering problems, such as the elastic wave transmission, can be described by the elastic wave equation. The efficient numerical algorithms for solving elastic wave equations are important. An ultra weak variational formulation based on the plane wave discretizations is proposed. First, by choosing the analytic solutions satisfying the homogeneous elastic wave equations and its adjoint equations to form the trial space and the test space, respectively, we obtain the equivalent Trefftz variational formulation; then we define the two-dimensional vector plane wave discretized trial space and test space to discretize the proposed continuous variational formulation. Numerical results based on Matlab have validated the proposed method.