In this paper torsion of prismatic bars considering elastic-plastic material behavior is studied. Based on the Saint-Venant displacement assumption and the Romberg-Osgood model for the stress-strain relation, the boundary value problem for stress function is formulated. In reality an area of cross section of a bar has two regions: elastic with linear governing equation and plastic with non-linear governing equation. In the solution procedure, the meshless procedure based on the Homotopy Analysis Method HAM connected with the Method of Fundamental Solutions (MFS) and Radial Basis Functions (RBF) is applied. The considered nonlinear partial differential equation (PDE) is transform into a hierarchy of linear inhomogeneous PDEs. The accuracy of the obtained approximate solution is controlled by the number of components of the calculate solution, while the convergence of the process is monitored by an additional parameter of the method. The advantage of the proposed meshless approach is that it does not require the generation of a mesh on the domain or its boundary, but only using a cloud of arbitrary located nodes
