The authors previously show that NI-RPIM solution of 3D tetrahedral cells [Yavuz and Kanber (2015)] includes unstable stress distributions. Therefore, in this study, the fluctuations in stresses are attempted to reduce using two different algorithms; Average stress distribution (ASD) in local support domain and LSS (least square stabilization) algorithms. NI-RPIM is improved with these algorithms to solve 3D solid mechanics problems with higher order Taylor series terms in nodal integration. Integration methodology is developed based on the study of [Liu et al. (2007)]. Tetrahedral integration cells are used in the solution of 3D elasto-static problems. Order of Taylor series terms is used up to 4^th order for ASD. Also effects of shape parameters ( and ) in RBF and support domain size (sd) are searched. The results are compared with available analytical solutions and discussed in detail.