Due to the increasing volume of spatio‐temporal data generated from remote sensing, sensor networks and computational simulation, there is a need for a generic, domain‐independent framework for spatio‐temporal data analysis. This research presents a generic set of data processing and manipulation tools for spatio‐temporal raster data called multidimensional map algebra (MMA). MMA is an extension of conventional map algebra that operates not only on data that are two‐dimensional in space but also on data that are: (1) one‐dimensional in time; (2) both two‐dimensional in space and one‐dimensional in time; (3) three‐dimensional in space; and (4) both three‐dimensional in space and one‐dimensional in time. MMA data types, neighborhoods, lags, and functions are presented, including rules for combining data types of different dimensionality within local, focal, and zonal functions. A prototype implementation in JAVA is provided as a demonstration and syntax specification for the functions. Challenges to continued development of MMA include performance and efficiency issues for processing very large multidimensional data sets.