The current paper presents the formulation of stochastic B-spline wavelet on the interval (BSWI) based wavelet finite element method (WFEM) for one dimensional (1D) and two dimensional (2D) problems in elasto-statics wherein, the spatial variation of modulus of elasticity is modelled as a homogeneous random field. Random field discretization is done using BSWI scaling functions. Perturbation approach is used to calculate the response statistics. The results are compared with that obtained from Monte Carlo simulation (MCS) and a parametric study is carried out by considering different coefficient of variation values by varying the standard deviation. For 1D problem in particular, results from proposed stochastic WFEM method are compared with those found using stochastic finite element method (FEM) wherein random field discretization is done using Lagrange shape functions. A comparative study of the computational time needed for the execution of perturbation approach and MCS based on WFEM and FEM is also performed. © 2019