The thesis proposes a numerical method called the combined successive over relaxation and fast Fourier transform convolution (CSF) method to solve the finite difference equations for the electrostatic field in a space periodic capacitance transducer (SPCT) and then to compute its response to a dielectric stimulus. The proposed method exploits the advantages of the successive over-relaxation (SOR) and FFT convolution techniques in a single algorithm. The overall field region is subdivided into two overlapping smaller regions: the first (nonhomogeneous) one is subjected to a given number of iterations using the SOR technique while the other is solved via the FFT convolution technique in an interdependent iterative approach. The process continues until an acceptably accurate solution is reached. For a test problem with Gaussian boundary conditions the CSF method has been found to be stable over certain ranges of its controlling parameters. Optimum performance was attainable for a given region in the space of these controlling parameters. The application of the CSF method to compute the SPCT fields has been investigated using a mesh of 110 by 32 nodes. The algorithm was programmed in Turbo Pascal using an IBM-compatible PC with a 486/DX4 processor and the method worked successfully for many combinations of the CSF controlling parameters. A reduction in computation time of about 40 percent was obtained in comparison with the SOR method when applied to the same problem. Three-dimensional plots of the SPCT fields are presented for the empty-channel case as well as for single dielectric stimulus in the channel. The capacitance waveforms produced by dielectric stimuli at different flying heights and of different sizes are also presented. The waveforms show that the response of the SPCT is spatially-biased towards particles flowing closer to the plane of sensing electrodes and that the resulting flow signal can be non-sinusoidal. This agrees with results obtained by workers using the SOR method.