We consider canonical systems (with $2p \times 2p$ Hamiltonians $H(x)\geq 0$) which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh–Weyl and spectral matrix functions and related $S$-nodes. Procedures for the construction of the fundamental solutions and solving inverse problems will be given. Expressions for the high energy asymptotics of the Weyl functions will be presented as well.