Source code summarization is the task of writing natural language descriptions of source code behavior. Code summarization underpins software documentation for programmers. Short descriptions of code help programmers understand the program quickly without having to read the code itself. Lately, neural source code summarization has emerged as the frontier of research into automated code summarization techniques. By far the most popular targets for summarization are program subroutines. The idea, in a nutshell, is to train an encoder-decoder neural architecture using large sets of examples of subroutines extracted from code repositories. The encoder represents the code and the decoder represents the summary. However, most current approaches attempt to treat the subroutine as a single unit. For example, by taking the entire subroutine as input to a Transformer or RNN-based encoder. But code behavior tends to depend on the flow from statement to statement. Normally dynamic analysis may shed light on this flow, but dynamic analysis on hundreds of thousands of examples in large datasets is not practical. In this paper, we present a statement-based memory encoder that learns the important elements of flow during training, leading to a statement-based subroutine representation without the need for dynamic analysis. We implement our encoder for code summarization and demonstrate a significant improvement over the state-of-the-art.