Transvascular and interstitial fluid movements are involved in many important biological processes such as convective macromolecular transport and contribute to the mechanical behavior of tissue. Although intimately coupled, there is a tendency in the literature to regard these two fluid-transport mechanisms separately; if the interaction is considered, the description is usually confined to the local level (e.g., transvascular or interstitial perivascular). A general framework presented here combines transvascular and interstitial fluid movement with the mechanics of soft tissue and integrates macro- and microscopic views of the phenomena. On the macroscopic level interstitial fluid transport is described by adapting the field equations of the poroelastic theory using average field variables defined on a scale of several blood vessel diameters (approximate to 1 mm), while transvascular transport is described by a generalized Starling’s law. As an example, the model equations have been specialized for a spherical solid tumor and an analytical solution is presented for the transient redistribution of interstitial fluid following a rapid change in vascular pressure or flow. The model describes the overall average profiles of the interstitial fluid pressure and velocity, as well as the dilatation, displacement and stress of the solid matrix. Moreover on a smaller length scale the model can describe the local fluid movement (perivascular) using the average field variables as boundary conditions. The basic theory provides new insight into understanding the fluid transport in biological tissues and a valuable tool for determining relevant fluid-transport parameters. Implications for improving drug delivery to solid tumors are also discussed.