This package provides a class and subclasses for storing non-scalar objects in matrix entries. This is akin to a ragged array but the raggedness is in the third dimension, much like a bumpy surface--hence the name. Of particular interest is the BumpyDataFrameMatrix, where each entry is a Bioconductor data frame. This allows us to naturally represent multivariate data in a format that is compatible with two-dimensional containers like the SummarizedExperiment and MultiAssayExperiment objects.