This paper describes the use of analytical solutions, accurate to first order in the maximum slow of the topography, for an elastic half space with surface topography to investigate the influence of valley shape and the regional state of stress on styles of coal mine roof failures described from the Appalachian plateau of the eastern United States. The basic solutions yield results for simple sinusoidal topography, and complicated valley shapes are simulated using Fourier series superposition of solutions. Different regional states of stress are simulated by varying a coefficient of lateral earth pressure. For a given state of regional stress, however, changes in valley form yield only small changes in the magnitude and distribution of the mean normal stress and maximum shear stress. Broad-floored valleys produce significantly different displacement and strain fields than do V-notch valleys, independently of the regional state of stress, because the perturbing effects of topography vary as a function of the reciprocal valley width.