Computational methods are slowly being adopted by the historical linguistics community. Their uses are many, from automatic cognate identification to phylogeny reconstruction. Their need is obvious, as more and more linguistic data become available in digital formats. This thesis applies LingPy, a computational toolkit for historical linguists, to data from Baltic and Slavic languages in an exploration of these language groups relationship to each other. Additionally, a new method for cognate identification, ALINE (Kondrak 2009), is integrated into LingPy, using phonetic features in the analysis. Considerable attention is given to the prior scholarship on the Balto-Slavic question and computational methods, to provide a foundation upon which the current analysis is built.