The thesis begins by describing the way in which gas phase chemistry of the interstellar medium can be modelled, and demonstrating the potential significance of chemical reactions on the surfaces of dust grains present in the gas. The dust also serves as the main shield against the interstellar ultraviolet continuum which influences the chemistry through photoionization and photodissociation reactions. The main part of this work involves the development of a method to evaluate radiative transfer into clumps in the diffuse interstellar medium and make use of such data for theoretical chemical models. The method handles clouds with axisymmetric shapes and therefore represents an improvement on previous techniques which model only plane-parallel clouds. The radiation field within diffuse clouds with spheroidal shapes is calculated and used to model the gas phase chemistry which would occur in such clouds. These results are of interest partly by comparison with previous results for slab-shaped clouds: they demonstrate the viability and value of 2D models of the interstellar medium, particularly with regard to examining the dynamical collapse of gas clouds. Finally, the possible influence of cloud shape on dust surface reaction rates is examined by calculating the grain charge distribution in the cloud models.