A recently developed numerical method is applied to the study of transient, nonlinear wave propagation in a laboratory flume. The nonlinear free surface boundary conditions and the wave generator boundary condition are expanded about the corresponding equilibrium positions by perturbation expansions. The Sommerfeld radiation condition applied on the downwave control surface is modified to incorporate a time-dependent celerity to account for transient effects. The boundary conditions are then satisfied to second order by a numerical integration in time, and the field solution at each time step is obtained by an integral equation method based on Green's theorem. The accuracy of the numerical solution is first assessed in term of the condition number. The propagation characteristics of regular and irregular waves are studied. To verify the numerical model, a series of laboratory tests have been performed. For the case of an irregular wave packet, the experimental results of the free surface elevations obtained at twelve different locations along the flume are compared with the corresponding numerical predictions and favourable agreement is indicated.