In first part, a solution scheme for the multiscale fluid transport equation of Singh et al. (2003a) was developed, which could be easily implemented in a commercial finite elements package for solving swelling/shrinking problems. The solution scheme was applied to drying of corn kernels. Laplace transformation was used to convert the integral part of the fluid transport equation to a set of differential equations. In materials undergoing volume change during drying, a moving mesh is needed in Eulerian coordinates, which is tedious to implement. An alternate method was used that involved transforming the equation to stationary Lagrangian coordinates. Once the equations were solved, the data was transformed back to the moving Eulerian coordinates during post-processing. Corn heterogeneity was taken into account by using different coefficient of diffusivity values for various corn components. To predict stresses, it was assumed that the shape of a kernel remains geometrically similar to its initial shape during drying. Using this assumption a relation between the strain tensor and volume fraction of water was developed. The viscoelastic stress strain constitutive equation was used to calculate the magnitude of stresses at different spatial locations inside a corn kernel. In the companion paper (part 2), the experimental validation of the solution, simulation results for various drying conditions and the practical implications are discussed. (C) 2011 Elsevier Ltd. All rights reserved.