This study serves three purposes: (i) to review a synthesis formula for simulation of band-limited stochastic processes based on the sinc expansion; (ii) to implement this synthesis formula in the tail-equivalent linearization method (TELM); and (iii) to demonstrate increased computational efficiency when the sinc expansion is implemented in this context. The proposed representation enables the reduction and control of the number of random variables used in the simulation of band-limited stochastic processes. This is of great importance for gradient-based reliability methods, including TELM, for which the computational cost is proportional to the total number of random variables. A direct application of the representation is used in TELM analysis. Examples of single-and multiple-degrees-of-freedom nonlinear systems subjected to Gaussian band-limited white noise simulated by use of sinc expansion are presented. The accuracy and efficiency of the representation are compared with those of the current time-domain discretization method. The analysis concludes by shedding light on the specific cases for which the introduced reduction technique is beneficial.