Longitudinal river profiles, where elevation of a river bed is plotted as a function of distance along the river bed, contain information about uplift rate. When a region adjacent to a reference level (e.g., sea level) is uplifted, a rapid change in gradient occurs near the river mouth. The erosional process causes this change in gradient to migrate upstream. Thus a river profile is effectively a ‘tape recording’ of the uplift rate history, provided that the erosional process can be adequately parameterized. Here, we use a non-linear equation to relate the shape of a river profile, z(x), to uplift rate history, U(t). If erosion is assumed to be dominated by knickpoint retreat, an inverse model can be formulated and used to calculate uplift rate histories. Our model builds upon standard stream profile analysis, which focuses on the relationship between profile slope and drainage area. We have applied this analytical approach to river profiles from the Bié Dome, Angola. Calculated uplift rate histories agree with independent geologic estimates.