The subaqueous evolution of alluvial deltas is sometimes driven by turbidity currents plunging along the delta foresets. In this paper,we examine howsuch hyperpycnal deltas evolve under conditions of steadily rising base level, associated either with a gradually filling reservoir, or with a rising sea level. The hyperpycnal delta evolution is envisioned as a one-dimensional diffusion process, with different diffusivities acting along the topset and foreset, and the resulting equation is solved by finite differences. Computations are first validated against analytical solutions derived earlier for the case of constant base level. Numerical simulations for the case of rising base level are then presented, and compared with small-scale laboratory experiments. The numerical, analytical and experimental results are found to be in good agreement with each other, and exhibit various features of interest. Like deltas evolving under homopycnal inflows, hyperpycnal deltas starting from a uniform slope first prograde, then retreat under the influence of a rising base level. Unlike the homopycnal case, however, a rising base level can cause erosion along the upper face of hyperpycnal foresets.We hypothesize that this could provide a mechanism for the incision of near-shore underwater canyons.