The issue to predict the behavior of building materials during wide horizons of time is still challenging. Experimental set-ups, since they require to perform tests for several years, are costly, never at the full scale and inconvenient. Building Performance Simulation (BPS) programs are designed to perform predictions on computational machines and cut experimental costs significantly. Nonetheless, in the recent review of state-of-the-art, it was indicated that despite the wide range of programs, there are still some drawbacks in terms of the accuracy and the high computational cost. This paper investigates the application of an innovative numerical method, called Super-Time-Stepping (STS) method. It allows performing accurate simulations with time-steps much larger than with standard explicit approaches. These "super" time-steps also enable us to reduce the computational cost. In addition to that, the design of the method allows easier application for models in higher dimensions and with nonlinear parameters. The efficiency of the method is tested on linear and nonlinear academic cases. Further study for the reliability of the model is performed on an experimental case study. The experiment has been carried out on a rammed earth wall during almost 14 months. Obtained data is presented in this article and implemented into proposed model. As a result of the case studies, it is shown that in comparison to the Euler explicit method, the STS methods can cut costs by more than five times while maintaining high accuracy and efficiency. A very fine analysis of the physical phenomena is also performed.