Flow and solute transport through porous media having strongly variable permeability were studied for parallel and convergent/divergent flows. The variation in hydraulic conductivity K causes (1) the fluid to flow through a porous medium along least resistive pathways and (2) solute dissolved in the fluid to be transported with widely different velocities. Numerical simulations were performed to study flow and solute transport in a three-dimensional heterogeneous porous block. It is found that for a strongly heterogeneous medium the particles (or solutes) travel through the medium along preferred flow paths, which we call channels. These channels possess hydraulic properties that are different from those of the global porous medium and which are invariant regardless of the direction from which the hydraulic gradient is applied to the porous block. The log-hydraulic conductivities along these channels have a greater mean value and a smaller standard deviation than for the global porous medium. These differences or ''shifts'' were calculated as a function of the hydraulic conductivity variance of the global porous medium. Tracer breakthrough curves for a pulse injection were also calculated. For small standard deviations of the global hydraulic conductivity distribution, a peak in the breakthrough curve is found which spreads out around its peak value as the standard deviation is increased. However, as the standard deviation is increased further, a new peak emerges at a much earlier time. This may be the result of increasing channeling effects at large standard deviations. For the case of a spherical pressure boundary around point tracer injection, the flow follows the usual divergent pattern only for small variations in hydraulic conductivity. When the standard deviation in log K is large, a significant portion of the flow becomes channelized; i.e., it tends toward a linear flow pattern. ¿ American Geophysical Union 1994