Molecular clouds are imperative to astronomy as the sites of all known star formation. The
problem of how molecular clouds are formed in spiral galaxies is approached numerically,
by modelling the response of a gas disk to a spiral potential. The importance of spiral
shocks is highlighted as a dominant formation mechanism for molecular clouds in grand
design galaxies, where a strong density wave is present. The spiral shock both increases
the density of the interstellar gas significantly, and produces structure in the spiral arms.
The gas evolves into discrete clumps, which are shown to contain substantial densities of
molecular hydrogen, and are therefore identified as molecular clouds. The formation of
these clouds requires that the interstellar medium (ISM) is cold and inhomogeneous. The
passage of an inhomogeneous gas distribution through a spiral potential further shows
that supersonic velocities are induced as the gas shocks. This can explain the velocity
dispersion relation observed in molecular clouds. Finally, the shearing of clumps of gas
in the spiral arms leads to the formation of inter-arm structures, which are commonly
observed in spiral galaxies.