In structural sensitivity analysis deterministic procedure is insufficient to provide complete information. Stochastic analysis is a holistic approach for computing response sensitivity considering uncertainties in structural parameters. Present study focuses an efficient stochastic finite element method for random response sensitivity analysis. Randomness of design variables is modeled through local averaging technique followed by Cholesky decomposition for digital simulation. Neumann expansion blended with Monte Carlo simulation (NE-MCS) has been employed in finite element solution for response sensitivity. Numerical examples are presented to illustrate the NE-MCS technique. Solution employing direct Monte Carlo simulation and perturbation are also presented to show the efficiency and accuracy of the proposed technique.