Collective flows of protons and $pi^{-}$-mesons are studied at the momenta of 4.2, 4.5 and 10 AGeV/c for p(C, Ta) and He(Li, C) interactions. The data were obtained from the streamer chamber (SKM-200-GIBS) and from the Propane Bubble Chamber (PBC-500) systems utilized at JINR. The method of Danielewicz and Odyniec has been employed in determining the directed transverse flow of particles. The values of the transverse flow parameter and the strength of the anisotropic emission were defined for each interacting nuclear pair. It is found that the directed flows of protons and pions decrease with increase of the energy and the mass numbers of colliding nucleus pairs. The $pi^{-}$-meson and proton flows exhibit opposite directions in all studied interactions, and the flows of protons are directed in the reaction plane. The Ultra-relativistic Quantum Molecular Dynamical Model (UrQMD), enlarged by the Statistical Multi-fragmentation Model (SMM), satisfactorily describes obtained experimental results.