[en] This thesis deals with the development and verification of numerical methods for the kinetic stability analysis of compact toroidal plasmas. These methods are applicable to the low-frequency stability analysis of plasmas characterized by ion gyroradii that are comparable to the plasma scale length. Examples of such plasmas include spheromaks, field-reversed mirrors, and theta pinches, and ion rings and layers. Kinetic effects due to the finite ion Larmor radius may be crucial to the description of the stability of these plasmas. The quaSi-neutral hybrid model is used to describe the plasma dynamics. The ions are treated in a fully kinetic manner using particle in-cell techniques, while the electrons are described as a fluid. The displacement current is neglected in Maxwell's equations. The equations are linearized about an axisymmetrical equilibrium, enabling the analysis of the three-dimensional linear stability. The simulation model includes plasmas which are surrounded by a vacuum region. A computer code was developed to integrate the linearized equations in time to detect instabilities. This code was verified extensively against known analytic or independent numerical results