In this paper, we report the procedure to analyse magnetic circuits and give the linear solutions on magnetic characteristics of the three-phase core-type transformer which is composed of the complicated magnetic paths. First, we explain the construction of cores investigated and normalize the sizes of a core. To analyse these magnetic circuits, we introduced the electrical eqcuivalent circuits and obtained the general fundamental equations for each core. Then, we drew the linear-numerical solutions using an electronic computer, and cleared the relationships between the sizes of a core and the amplitudes and phase angles of fluxes in magnetic paths. Related with the above facts, we investigate the influence of these sizes on the core loss using cores of various quality.