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This report focuses on modelling the OSIRIS neutron-backscattering instrument using Monte Carlo methods with the use of the McStas software package. The aim is to match the experimental energy resolution of OSIRIS and thus be able to simulate the instrument in order to investigate its various properties and performance characteristics. Furthermore, understanding quantitatively how different components of OSIRIS contribute towards its resolution function will provide insight into potential upgrade possibilities of the instrument. The simulated energy resolution FWHM values of 23.7 μeV for PG002 and 96.3 μeV for PG004 show a good agreement with the experimental results of 25.0 μeV for PG002 and 99.5 μeV for PG004 and are only 5% and 3% lower respectively.