In the paper, the static sensitivity of complex structures with respect to random design parameters is presented. Using the adjoint system method, based on the mean-point second-order perturbation method, the first two probabilistic moments of time-independent sensitivity are formulated with means and cross-covariances of random design parameters as the input data. It enables one to obtain the second-order accuracy of the solution. The presented formulations are illustrated by a number of numerical examples. The influence of finite element mesh density for the obtained results is discussed using the analysis of the spatial bar dome.