The higher order multipoint meshless method [2] was developed recently. It is based on the old Collatz higher-order multipoint idea [1] and the meshless finite difference method (MFDM) [3]. Besides development of the multipoint MFDM for the analysis of boundary value problems given in the strong formulation, the multipoint method was also extended to the various weak and global-local formulations. Two versions of the multipoint MFDM – the general and the specific ones are distinguished. Beside the improved solution quality, the general multipoint version is potentially wide range of applications, including nonlinear ones [4]. The paper is focused on application of the multipoint method for the nonlinear analysis [5], especially for solving physically nonlinear problems. The general approach of the multipoint MFDM has some advantages for the solution of the various types of the nonlinear boundary value problems. The aspects of the method application were investigated. The numerical results obtained so far for several tests are very encouraging taking into account both their precision and efficiency. The approach is under current development.