Historical time series show that industrial uses for sulfur exhibit diverse trends and significant fluctuations. A plausible reason for this behavior of industrial demand is the presence of alternative inputs used to replace sulfur. On the other hand, sulfur may replace existing inputs used by respective industries because of a more favorable relative price or because of its superior qualities. This study makes use of regression and analysis to examine direct demand and cross-demand for sulfur and alternative inputs. The major industries that currently choose between sulfur and alternative inputs include the following: chemicals, inorganic pigments, pulping processes, nonferrous ores leaching, and iron and steel pickling. Some of these industries show an increasing demand for sulfur while others show a declining demand. By examining and evaluating direct price elasticities and cross price elasticities, degree of substitution can be detected. Proper evaluation of the statistical results lends background support for action programs for the sulfur industry to promote uses where alternative inputs are at an economic disadvantage, and withdrawal from those uses where alternative inputs have a pronounced economic advantage.