  We present Smoothed Particle Hydrodynamics (SPH) simulations of molecular
cloud formation in spiral galaxies. These simulations model the response of a
non-self-gravitating gaseous disk to a galactic potential. The spiral shock
induces high densities in the gas, and considerable structure in the spiral
arms, which we identify as molecular clouds. We regard the formation of these
structures as due to the dynamics of clumpy shocks, which perturb the flow of
gas through the spiral arms. In addition, the spiral shocks induce a large
velocity dispersion in the spiral arms, comparable with the magnitude of the
velocity dispersion observed in molecular clouds. We estimate the formation of
molecular hydrogen, by post-processing our results and assuming the gas is
isothermal. Provided the gas is cold ($T\le100$ K), the gas is compressed
sufficiently in the spiral shock for molecular hydrogen formation to occur in
the dense spiral arm clumps. These molecular clouds are largely confined to the
spiral arms, since most molecular gas is photodissociated to atomic hydrogen
upon leaving the arms.
