Infrared detected materials, such as Hg1-xCdxTe, Hg1-xZnxTe have energy gaps almost linearly proportional to their composition. Due to the wide separation of liquidus and solidus curves of their phase diagrams, compositional segregation exists in both axial and radial directions of crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms, which affect lateral segmentation in order that large radially uniform composition crystals can be produced. Following the Coriell, et al. treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on lateral composition distribution. The model is considered to be a cylindrical system with azimuthal symmetry and a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessel functions. The results show that melt-solid interface shape has a dominant effect on the lateral composition distribution of these systems. For small values of β, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the product of β and (1-k), where β-Vr/D, with V as growth velocity, R as the sample radius, D as the diffusion constant and k as the distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.