During hydraulic fracturing, thousands of barrels of fluid are injected into the rock surrounding the created fractures. Observations show that later during flowback, only a small fraction of the injected fluid volume is produced back. In tight naturally fractured formations, this can be explained by the leading role of preexisting rock discontinuities in the transport of fluids in such rocks. In this work, we investigate the mechanics of injected fluid flow in and out of preexisting rock discontinuities during a typical operational sequence of fracturing treatment, well shut-in and flowback. The mechanics of fluid flow in compliant discontinuities, where conductivity is sensitive to stress changes, is different from that in a stiff rock matrix. To understand and quantify rock pressurization, fluid leakoff and flowback rates, we develop a numerical model of fluid flow in a system of arbitrarily oriented discontinuities. Using this model, we predict spatial distribution of the injected fluid in a naturally fractured rock at any time after the beginning of the fracturing treatment as well as after the well shut-in and during flowback. The model explains the trapping of injected fluid in the discontinuities during production. We validate the model by comparison with field data and provide rough estimates of the volumetric fracturing fluid accumulation in the rock discontinuities after the treatment. The spatial extent of rock "flooding" around hydraulic fractures is found to depend on the density and orientation of rock discontinuities.