A major challenge in studying impact problems analytically is solving the governing equations of impact events, which are mostly in the form of nonlinear ODEs. This paper focuses on the solution of nonlinear models for impact problems in asymptotic cases, where local indentation is significant. The asymptotic cases consist of both half-space and infinite plate impacts, which cover a wide range of practical impact events. A so-called force–indentation linearisation method (FILM), first described in a previous study, is reformulated here in a more general form in order to broaden its scope of application. The generalisation of the FILM facilitates stable and convergent solutions even when complex nonlinear contact models are used to estimate the impact force. Simulations based on the FILM approach are validated using numerical solutions.