  We give a simple topological construction of the Burau representations of the
loop braid groups. There are four versions: defined either on the non-extended
or extended loop braid groups, and in each case there is an unreduced and a
reduced version. Three are not surprising, and one could easily guess the
correct matrices to assign to generators. The fourth is more subtle, and does
not seem combinatorially obvious, although it is topologically very natural.
