The investigation reported in this paper is to further improve the effectiveness of some stochastic direct integration schemes. These stochastic direct integration schemes were proposed to compute response statistics, such as mean squares and variances of generalized displacements, of large discretized structures undergoing large non-linear deformation and under non-stationary random excitation. First of all, the stochastic Newmark method is extended to include the stochastic as well as the deterministic excitations. Next, a correction factor that is to be applied to the discrete white noise is introduced. The stability criterion is then examined. The advantage of introducing such a correction factor is that one is not limited to those time step sizes that have been found to yield accurate response statistics in previous investigations. Instead, one can choose a time step size in the way he may in an analysis using the deterministic Newmark method. The correction factor is determined based on this chosen time step size, thus providing the flexibility in balancing the needs of accuracy and effectiveness. Subsequently, the hybrid strain based three-noded flat triangular shell element, single- or multi-layered, is employed to model selected plate structures. These numerical examples demonstrate the accuracy and effectiveness of the proposed methodology.