In this paper, two simplified models of edge localized mode (ELM) power exhaust are developed, one based on the kinetic and the other on the fluid treatment of parallel losses. These models are found to capture many (though not all) of the salient features of kinetic simulations at substantial savings in both cost and complexity (CPU time in seconds versus days), making them ideal as real time interpretive tools or as modules in non-linear MHD, transport and/or turbulence codes. The kinetic model offers analytic expressions for the ion and electron powers deposited on the divertor, parametrized in terms of transient sheath energy transmission coefficients gamma(i) and gamma(e), in good agreement with particle-in-cell simulations. The fluid model successfully reproduces ELM filament densities and electron energies measured at the outer poloidal limiter on JET, as well as recent measurements of ELM filament ion energies in the JET far-scrape-off layer (SOL). Taking confidence from this favourable comparison, the same model is then used to predict ion impact energies due to the incidence of Type-I ELM filaments on the ITER limiter. Although the models are applied here exclusively to ELMS, they have a potential application to other tokamak transients, such as intermittent SOL bursts and the disruption thermal quench.