The bacterium Listeria monocytogenes uses the energy of the actin polymeriz
ation to propel itself through infected tissues. In steady state, it contin
uously adds new polymerized filaments to its surface, pushing on its tail,
which is made from previously cross-linked actin filaments. In this paper w
e introduce an elastic model to describe how the addition of actin filament
s to the tail results in the propulsive force on the bacterium. Filament gr
owth on the bacterial surface produces stresses that are relieved at the ba
ck of the bacterium as it moves forward. The model leads to a natural compe
tition between growth from the sides and growth from the back of the bacter
ium, with different velocities and strengths for each. This competition can
lead to the periodic motion observed in a Listeria mutant.