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Monte Carlo simulation programs based on the Geant4 package have become indispensable tools in modern particle physics. Following the advances in muon-spin rotation (μSR) instrumentation we have written a simulation code, MUSRSIM, currently in use in the development and optimisation of contemporary μSR spectrometers. MUSRSIM was employed for optimising the design of a new type of avoided level crossing (ALC) instrument, which is characterised by the exclusive use of Geiger-mode avalanche photodiodes instead of the standard photomultiplier tubes. The simulation code allowed us to study in detail the influence of the detector geometry, of the initial muon beam properties, and (to a limited extent) of the electronic signal processing on the predicted spectra. The good agreement between the simulation results and the measured data, validates MUSRSIM as a reliable software tool also for future instrument development work.