Explosive activity and lava dome collapse at stratovolcanoes can lead to pyroclastic density currents (PDCs; mixtures of volcanic gas, air, and volcanic particles) that produce complex deposits and pose a hazard to surrounding populations. Two-dimensional computer simulations of dilute PDCs (characterized by a turbulent suspended load and deposition through a bed load) show that PDC transport, deposition, and hazard potential are sensitive to the shape of the volcano slope (profile) down which they flow. We focus on three generic volcano profiles: straight, concave-upward, and convex-upward. Dilute PDCs that flow down a constant slope gradually decelerate over the simulated run-out distance (5 km in the horizontal direction) due to a combination of sedimentation, which reduces the density of the PDC, and mixing with the atmosphere. However, dilute PDCs down a concave-upward slope accelerate high on the volcano flanks and have less sedimentation until they begin to decelerate over the shallow lower slopes. A convex-upward slope causes dilute PDCs to lose relatively more of their pyroclast load on the upper slopes of a volcano, and although they accelerate as they reach the lower, steeper slopes, the acceleration is reduced because of the upstream loss of pyroclasts (lower density contrast with the atmosphere). Dynamic pressure, a measure of the damage that can be caused by PDCs, reflects these complex relations.