Rates of transcription elongation vary within and across eukaryotic gene bodies. Here, we introduce new methods for predicting elongation rates from nascent RNA sequencing data. First, we devise a probabilistic model that predicts nucleotide-specific elongation rates as a generalized linear function of nearby genomic and epigenomic features. We validate this model with simulations and apply it to public PRO-seq (Precision Run-On Sequencing) and epigenomic data for four cell types, finding that reductions in local elongation rate are associated with cytosine nucleotides, DNA methylation, splice sites, RNA stem-loops, CTCF (CCCTC-binding factor) binding sites, and several histone marks, including H3K36me3 and H4K20me1. By contrast, increases in local elongation rate are associated with thymines, A+T-rich and low-complexity sequences, and H3K79me2 marks. We then introduce a convolutional neural network that improves our local rate predictions. Our analysis is the first to permit genome-wide predictions of relative nucleotide-specific elongation rates.