  The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on
$n$ elements generated by prefix reversals. $P_n$ has been shown to have
properties that makes it a useful network scheme for parallel processors. For
example, it is $(n-1)$-regular, vertex-transitive, and one can embed cycles in
it of length $\ell$ with $6\leq\ell\leq n!$. The burnt pancake graph $BP_n$,
which is the Cayley graph of the group of signed permutations $B_n$ using
prefix reversals as generators, has similar properties. Indeed, $BP_n$ is
$n$-regular and vertex-transitive. In this paper, we show that $BP_n$ has every
cycle of length $\ell$ with $8\leq\ell\leq 2^n n!$. The proof given is a
constructive one that utilizes the recursive structure of $BP_n$. We also
present a complete characterization of all the $8$-cycles in $BP_n$ for $n \geq
2$, which are the smallest cycles embeddable in $BP_n$, by presenting their
canonical forms as products of the prefix reversal generators.
