The aim of the submitted proposal is to get financial support for development of Monte Carlo methods for simulations of complex neutron optical systems, including their experimental validation and application to the research of dispersive multiple reflections of neutrons in elastically bent crystals. The new methods will be implemened in existing and well established software package RESTRAX, which has been developed at the NPI Řež. The results of experimental research of multiple Bragg reflections supported by Monte Carlo simulations will be employed in the development of high-resolution monochromators and analyzers. The ultimate goal of the proposed research is twofold: (a) Creation of an easy to use, validated and efficient software for modeling and optimization of neutron spectrometers employing advanced neutron optics elements and for data analysis; (b) Development and tests of dispersive multiple reflection monochromators suitable for ultra-high resolution measurements.