Intense underwater sounds caused by military sonar, seismic surveys, and pile driving can harm acoustically sensitive marine mammals. Many jurisdictions require such activities to undergo marine mammal impact assessments to guide mitigation. However, the ability to assess impacts in a rigorous, quantitative way is hindered by large knowledge gaps concerning hearing ability, sensitivity, and behavioral responses to noise exposure. We describe a simulation-based framework, called SAFESIMM (Statistical Algorithms For Estimating the Sonar Influence on Marine Megafauna), that can be used to calculate the numbers of agents (animals) likely to be affected by intense underwater sounds. We illustrate the simulation framework using two species that are likely to be affected by marine renewable energy developments in UK waters: gray seal (Halichoerus grypus) and harbor porpoise (Phocoena phocoena). We investigate three sources of uncertainty: How sound energy is perceived by agents with differing hearing abilities; how agents move in response to noise (i.e., the strength and directionality of their evasive movements); and the way in which these responses may interact with longer term constraints on agent movement. The estimate of received sound exposure level (SEL) is influenced most strongly by the weighting function used to account for the specie's presumed hearing ability. Strongly directional movement away from the sound source can cause modest reductions (~5 dB) in SEL over the short term (periods of less than 10 days). Beyond 10 days, the way in which agents respond to noise exposure has little or no effect on SEL, unless their movements are constrained by natural boundaries. Most experimental studies of noise impacts have been short-term. However, data are needed on long-term effects because uncertainty about predicted SELs accumulates over time. Synthesis and applications. Simulation frameworks offer a powerful way to explore, understand, and estimate effects of cumulative sound exposure on marine mammals and to quantify associated levels of uncertainty. However, they can often require subjective decisions that have important consequences for management recommendations, and the basis for these decisions must be clearly described.