The purpose of this paper is to present stress-intensity factor influence coefficients for a wide range of semi-elliptical surface cracks on the inside or outside of a cylinder. The crack surfaces were subjected to four stress distributions: uniform, linear, quadratic, and cubic. These four solutions can be superimposed to obtain stress-intensity factor solutions for other stress distributions, such as those caused by internal pressure and by thermal shock. The results for internal pressure are given herein. The ratio of crack depth to crack length from 0.2 to 1; the ratio of crack depth to wall thickness ranged from 0.2 to 0.8; and the ratio of wall thickness to vessel radius was 0.1 or 0.25. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employ singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated from a nodal-force method. The present results were also compared to other analyses of surface cracks in cylinders. The results from a boundary-integral equation method agreed well (±2 percent), and those from other finite-element methods agreed fairly well (±10 percent) with the present results.