Electrostatic and magnetostatic particle simulation models have been developed and tested for a magnetically confined plasma near thermal equilibrium. The model makes use of a three-dimensional grid elongated in the direction of a magnetic field to simulate plasma confinement devices. Linear interpolation is used on a two-dimensional grid perpendicular to a magnetic field while quadratic or cubic interpolation is used in the direction of the magnetic field. It is found that energy conservation is good and the fluctuation spectra for the electric and magnetic fields agree with theoretical predictions. The model presented here may be used as an alternative method to simulate a laboratory device along with the hybrid model which makes use of the combination of a two-dimensional spatial grid and an eigenfunction expansion along the main magnetic field.