Engineers of off-road equipment, on-road vehicles, pavement, and tires must assess the roughness of a terrain surface for the design of their products. The International Roughness Index (IRI), a standardized means of assessing longitudinal road roughness, quantifies roughness based on the average suspension travel for a particular vehicle at a prescribed speed. The Discrete Roughness Index (DRI) developed in this work address fundamental limitations of the IRI. Specifically, the DRI is calculated for each discretely measured location along a terrain surface and is applicable to vehicles traveling at varying speeds and using parameters other than the Golden Quarter-Car on which the IRI is based. The development of the DRI begins with a consistent discretization of the terrain surface, vehicle response, and the IRI. Next the Fractional Response Coefficient is developed, the properties of which are critical in the development of the DRI. The DRI is developed and its properties are discussed through theory and simulation of the ASTM E1926-08 profile. One important property of the average DRI is that it converges to the IRI as the distance between sampled points becomes smaller, for the particular case when the Golden Quarter-Car model is simulated at 80 kph. The DRI is not an alternative to the standard IRI, therefore, but a widely applicable roughness measure of which the standard IRI is a single specialized application. / Master of Science