A hallmark of the infectious cycle for many RNA viruses parasitizing multicellular hosts is the need to invade and successfully replicate in tissues that comprise a variety of cell types. Thus, multicellular hosts represent a heterogeneous environment to evolving viral populations. To understand viral adaptation to multicellular hosts, we took a double approach. First, we developed a mathematical model that served to make predictions concerning the dynamics of viral populations evolving in heterogeneous environments. Second, the predictions were tested by evolving vesicular stomatitis virus in vitro on a spatially structured environment formed by three different cell types. In the absence of gene flow, adaptation was tissue-specific, but fitness in all tissues decreased with migration rate. The performance in a given tissue was negatively correlated with its distance to the tissue hosting the population. This correlation decreased with migration rate.