Laser cladding techniques have recently enjoyed attention in preparing in-situ novel surface clad alloys with extended solid solution. Mass transport involved in this process is rather intriguing since it plays the major role in producing new materials without being restricted by equilibrium phase diagram. Although earlier work has identified convection as the dominant factor for homogeneous liquid metal composition, very little is understood about the solute redistribution at the solid-liquid interface under such non-equilibrium conditions. In this paper, a mathematical model is presented for determining the composition of extended solid solution formed due to rapid cooling in laser cladding. This model considers a diffusion mechanism for mass transport in a one-dimensional semi-infinite molten pool of the cladding material from which heat is removed by conduction through a one-dimensional semi-infinite solid substrate. The rate of solidification was obtained by modeling the cooling process as a composite medium heat transfer problem, and the discontinuity of the concentration field was simulated using a nonequilibrium partition coefficient. A non-similar exact solution for the mass transport equation was obtained using a set of similarity variables derived using Lie group theory.