For a given solution of Riemann problem for elastic perfectly plastic solid Euler equations ignoring vacuum, we give condition that the initial physical quantity should be satisfied and prove completeness of the initial condition corresponding to a particular solution. That is, for any given initial physical quantity, it corresponds to only one solution of Riemann problem. Therefore, the solution of Riemann problem can be judged directly and accurately according to the initial condition in the design of exact or approximate Riemann solvers.