The current work proposes novel stochastic meshless methods for the analysis of linear and nonlinear problems in structural mechanics which can take care of uncertainties in material property and loading when they appear as random variables or homogeneous random fields. The study suggests an improved response function based stochastic meshless method for the analysis of linear elastic problems. Further, the study also proposes a simple and efficient stochastic meshless method for the analysis of linear eigenvalue problems in structural mechanics. A high dimensional model representation based stochastic meshless technique is proposed in the current study for the analysis of geometric nonlinear problems in solid mechanics. A few numerical examples are solved to validate the proposed method by comparing the results with the direct Monte Carlo simulation or other existing methods. Further, the computational efficiency of the proposed methods is also established.