The general purpose neutron–photon–electron Monte Carlo N-Particle code, MCNP TM , has been used to simulate the neutronic characteristics of the on-site laboratory passive neutron coincidence counter to be installed, under Euratom Safeguards Directorate supervision, at the Sellafield reprocessing plant in Cumbria, UK. This detector is part of a series of nondestructive assay instruments to be installed for the accurate determination of the plutonium content of nuclear materials. The present work focuses on one aspect of this task, namely, the accurate calculation of the coincidence gate utilisation factor. This parameter is an important term in the interpretative model used to analyse the passive neutron coincidence count data acquired using pulse train deconvolution electronics based on the shift register technique. It accounts for the limited proportion of neutrons detected within the time interval for which the electronics gate is open. The Monte Carlo code MCF, presented in this work, represents a new evaluation technique for the estimation of gate utilisation factors. It uses the die-away profile of a neutron coincidence chamber generated either by MCNP TM , or by other means, to simulate the neutron detection arrival time pattern originating from independent spontaneous fission events. A shift register simulation algorithm, embedded in the MCF code, then calculates the coincidence counts scored within the electronics gate. The gate utilisation factor is then deduced by dividing the coincidence counts obtained with that obtained in the same Monte Carlo run, but for an ideal detection system with a coincidence gate utilisation factor equal to unity. The MCF code has been benchmarked against analytical results calculated for both single and double exponential die-away profiles. These results are presented along with the development of the closed form algebraic expressions for the two cases. Results of this validity check showed very good agreement. On this basis, previously published analytical results for the double exponential case are thought to be in error. As derived analytically, the numerical calculations have been found to be both independent of the detector's efficiency and of the spontaneous fission neutron multiplicity distribution used in the Monte Carlo calculations. Extension of the MCF calculations to multiplicity counting, and in particular to triple coincidence counting, confirmed that, for a single exponential die-away profile, the triple gate utilisation factor is equal to the square of the real gate utilisation factor. For other profiles this relation no longer holds. An analytical expression is given for the case of a double exponential profile. Comparison of the MCF results with earlier calculated estimates of the gate utilisation factor for the on-site laboratory neutron coincidence chamber showed a significant difference. Use of the MCF results led to much better agreement between the observed and calculated specific reals coincidence rate of the on-site laboratory counter for the assay of plutonium samples. Moreover, the present work constitutes a further step towards the improvement of the accuracy of absolute Monte Carlo calculations for active or passive neutron measurements of nuclear materials.