Accidents occur when the circumstances (i.e. the inputs) leading up to an accident map through the physical processes involved, to produce an undesirable result, namely the accident (i.e., the outputs). What the accident reconstructionist has to work with is the evidence left behind, and he then strives to determine the circumstances that led to the accident, based upon that evidence. In accident investigation there is often a deficit of physical evidence, and it is impossible, based on the available physical evidence alone, to pinpoint the circumstances that led to the accident. In practice, computer programs are often used to run simulations to find a set (or sets) of circumstances that is consistent with the evidence, and then the discovered set (or sets) of circumstances is presented as the answer. But this approach ignores some important questions related to whether the mapping being used (e.g., the computer simulation) is invertible and whether the circumstances leading to the evidence can be identified in a unique way, or whether the mapping is not invertible and the most that can be achieved is to identify whole sets in the input space of circumstances that might have led to the accident. Analysis offers the tools to probe such questions.