  We present exact calculations of flow polynomials $F(G,q)$ for lattice strips
of various fixed widths $L_y$ and arbitrarily great lengths $L_x$, with several
different boundary conditions. Square, honeycomb, and triangular lattice strips
are considered. We introduce the notion of flows per face $fl$ in the
infinite-length limit. We study the zeros of $F(G,q)$ in the complex $q$ plane
and determine exactly the asymptotic accumulation sets of these zeros ${\cal
B}$ in the infinite-length limit for the various families of strips. The
function $fl$ is nonanalytic on this locus. The loci are found to be noncompact
for many strip graphs with periodic (or twisted periodic) longitudinal boundary
conditions, and compact for strips with free longitudinal boundary conditions.
We also find the interesting feature that, aside from the trivial case $L_y=1$,
the maximal point, $q_{cf}$, where ${\cal B}$ crosses the real axis, is
universal on cyclic and M\"obius strips of the square lattice for all widths
for which we have calculated it and is equal to the asymptotic value $q_{cf}=3$
for the infinite square lattice.
