This paper presents a generalized two-dimensional analytical solute transport model with unidirectional flow field from time- and space-dependent sources in a bounded homogeneous medium using the flux-type (or third-type or Cauchy) boundary condition at the inlet location of the medium. The solute transport equation incorporates terms accounting for advection, dispersion, linear equilibrium sorption, and first-order decay. General solutions were determined for arbitrary input boundary conditions with the help of Fourier analysis and Laplace transform techniques. After presenting a generally applicable solution, special solutions are given for a single and two finite sources having different inlet solute flux distributions. The expressions for convective-dispersive flux components are also derived. Expressions for concentration distribution and convective-dispersive flux components for steady state transport case are also presented. Comparison of the results of this analytical model and a finite difference numerical model showed very good agreement. The solutions may be used for predicting solute concentrations in a unidirectional porous media flow field as well as in rivers and canals. The solutions may also be used for verification of more comprehensive numerical models, and laboratory or field determination of solute transport parameters. ¿ American Geophysical Union 1993