The Monte Carlo method is considered to be the most accurate approach for simulating neutron transport in a reactor core, since it requires no or very few approximations and can easily handle complex geometric shapes (no discretisation is involved). A particular challenge for Monte Carlo simulation in reactor physics applications is to calculate the impact of a small model change: formally, this involves calculating the derivative of an observable with respect to a given parameter. In a Monte-Carlo code, the statistical uncertainty is considerably amplified when calculating a difference between similar values. Consequently, several Monte Carlo techniques have been developed to estimate perturbations directly. However, the question of calculating perturbations induced by a change in reactor geometry remains fundamentally an open problem. The aim of this thesis is to investigate the advantages and shortcomings of existing geometric perturbation methods and to propose new ways of calculating the derivatives of reactor parameters with respect to changes in its geometry. The challenge is twofold. Firstly, it will be necessary to design algorithms that can efficiently calculate the geometric perturbation itself. Secondly, the proposed approaches will have to be adapted to high-performance computing environments.