SUMMARY
Meshless method choosing Heaviside function as a test function for solving simply supported thin plates under various loads as well as on regular and irregular domains is presented in this paper. The shape functions using regular and irregular nodal arrangements as well as the order of polynomial basis choice are constructed by moving Kriging interpolation. Alternatively, two-field-variable local weak forms are used in order to decompose the governing equation, biharmonic equation, into a couple of Poisson equations and then impose straightforward boundary conditions. Selected mechanical engineering thin plate problems are considered to examine the applicability and the accuracy of this method. This robust approach gives significantly accurate numerical results, implementing by maximum relative error and root mean square relative error.