A method for simulating the transient responses of networks containing lossless transmission lines and lumped parameter elements of circuits, both linear and nonlinear, has been developed and investigated. The method combines the technique of network analysis and that of modal decomposition of transmission lines. A prototype computer simulation program, called UANTL, based on the developed algorithm has been implemented. Several example networks have been simulated using this program. The results have been compared with those generated by the well known circuit simulator program called SPICE. UANTL has shown several advantages over SPICE in simulating the transient responses of networks containing transmission lines. A description of the prototype version of UANTL and a summary of the results of numerical experiments are included.