Abstract: Kriging surrogate model is suggested to approximate the solutions of bimodular plane elastic problems. By utilizing a smoothed constitutive equation, finite element method, and the Latin hypercube sampling skill, a Kriging model based approximate numerical solution is presented to surrogate the FEM based solution of bimodular trusses and 2D plane problems. The impacts of sample numbers and problem scales on the computing accuracy/efficiency of the surrogate model are investigated. Numerical tests indicate that the proposed approach is capable of providing an approximate numerical solution with a reasonable computing accuracy for the bimodular plane problem, and considerable amount of computing time can be saved particularly when the solutions of direct bimodular problems are continually required and the problem scale is relatively large. The work presented in this paper is significantly valuable for saving computing time in solving the inverse bimodular problem and bimodular optimization problem.