This thesis deals with the time-domain analysis of switched linear networks and investigates inherent problems which have to be considered when analyzing this class of networks. Computer simulation requires the use of numerical methods and we focus on the transmission -line modelling technique (TLM) and the numerical inverse Laplace transform. A general approach based on the one-graph modified nodal description is given which allows the formulation of circuit equations of a TLM-modelled circuit by inspection. The numerical equivalence of TLM and trapezoidal rule has been found and a proof is given. A variable step size simulator has been developed based on the 4th order numerical inverse Laplace transform. The properties of this method are reviewed and its limitations are discussed. Simulation results are given to illustrate capabilities of the simulator.