Abstract: In order to achieve non-iterative algofithm of the elasto-plastic problems,thelinear complementary equations are derived from a simple and stict way in this paper.Compared with otlier non-iterative methods, the scale of linear complementary problemgiven here is much smaller. The well-posedness of the solution is discussed.The practicalalgorithm for solving engineering problems is given, and two examples are also calculated.