Glasses corresponding in composition to BaMnSiO4 and BaMnSi2O6 crystalline phases synthesized previously, have been obtained in the region with low SiO2 content of the BaO-MnO-SiO2 system. The glass structures were investigated by electron spin resonance, ultraviolet-visible and infrared spectroscopy, X-ray diffraction methods, etc. The trend to a complex ortho-silicate structure owing to the transformations into diortho-groups and silicate rings, has been established. The R(1) (0.186-0.177 nm) maxima of the total pair correlation functions are related to the mean Si-O and Mn-O distances, while the RP (0.283-0.278 nm) maxima refer to the Ba-O distance. Conclusions are drawn concerning the formation of Mn-O and Ba-O polyhedra. It is assumed that several kinds of structural polyhedra participate in the formation of the glass network.