  Given a presentation for a rack $\mathcal R$, we define a process which
systematically enumerates the elements of $\mathcal R$. The process is modeled
on the systematic enumeration of cosets first given by Todd and Coxeter. This
generalizes and improves the diagramming method for $n$-quandles introduced by
Winker. We provide pseudocode that is similar to that given by Holt for the
Todd-Coxeter process. We prove that the process terminates if and only if
$\mathcal R$ is finite, in which case, the procedure outputs an operation table
for the finite rack. We conclude with an application to knot theory.
