We present a theoretical model of a superconducting kinetic inductance detector which promises high sensitivity and energy resolution from submillimetre to X-ray wavelengths. Cooper-pair breaking photons are absorbed in a superconductor, exciting quasiparticles which change the surface inductance. By arranging the detector in a resonant circuit we can measure the resulting phase-shift of a microwave probe signal. Software has been created to model the superconducting characteristics of the detector and its behaviour when a photon is absorbed. The model predicts the position sensitivity of the detector and calculates how quasiparticles diffuse and recombine to a thermal background level. This temporal evolution of quasiparticle dynamics gives rise to a measurable phase-shift pulse, which will allow the energy and time of a photon to be measured. Pulse shapes have been simulated for photon energies of 1-5 keV being absorbed at the sensitive ground-end of the detector.