This appears to be the first publication to rigorously develop mathematical relationships for the mass loss of common three-dimensional shapes as they progressively diminish in size. Equations were derived for the erosion of the surfaces of circular and square objects due to biodegradation, i.e., the decrease in volume caused by the high catalytic activity of enzymes secreted by microorganisms attached to the object’s surfaces. Surface erosion is the dominant mode of biodegradation for polyhydroxyalkanoate (PHA) objects resting on the ocean floor. Although the derivations were motivated by a need to assess the time-varying biodegradation and ultimate disintegration of PHA tubes and straws in the benthic environment, generality was maintained during the mathematical development such that the resulting equations are also applicable to other degrading circular and square objects including cylindrical rings, discs, and rods, and square plates, cubes, and prisms. Surface erosion is dominant for some in vivo biodegrading medical devices, so it is believed that the equations will also be useful in the biomedical field. In the theory, surface erosion is expressed in terms of the ratio of the instantaneous mass to the initial mass. The value of this ratio and the relative dimensions of the object establish a surface erosion function and its evolution over the lifetime of the object.