This paper considers an issue of selecting the number of structural breaks in $p$th order vector autoregressive (VAR($p$)) processes by model selection criteria. We establish Akaike's information criterion (AIC) for VAR($p$) processes with multiple structural changes, extending the result of Ninomiya (2005, 2006). We treat the number of structural changes, $m$, as a parameter to be estimated and show that the penalty term of AIC related with $m$ is not $2m$ as in the conventional AIC but it should be $6m$. We also derive Mallows' $C_{p}$ criterion. The finite sample performance of these model selection criteria is investigated through Monte Carlo simulations.