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Triangle impulse responses (TIRs) for lossy transmission lines are accurately calculated using both an inverse fast Fourier transform algorithm and an accelerated inverse Laplace transform algorithm. Frequency dependent transmission line parameters, i.e., R, L, G, and C, are employed to model the skin effect and the frequency dependent electrical properties of the substrate material. The calculated TIR can be further used to carry out time domain simulations for a large number of lossy transmission lines. Frequency dependent line parameters, R, L, G, and C should be used in specific cases to assure the causality of signal waveform, the accuracy of the time delay, and the amplitude of the waveform evaluations in the time domain.