An epoxy resin film which is so strong as to have a tensile strength of not less than 10 MPa and an elongation of not less than 5% is formed by using a substantially linear high molecular weight epoxy resin which is synthesized by polymerizing a difunctional epoxy resin having two epoxy groups per molecule and a dihydric phenol in an aprotic polar solvent, in the presence of a solvent, at a reaction temperature ranging from 80.degree. to 130.degree. C., the difunctional epoxy resin and the dihydric phenol being used in quantities which provide a ratio of phenolic hydroxyl groups to epoxy groups of from 1:0.9 to 1:1.1 and a proportion of the total of them of at most 50% by weight based on the total of them and the aprotic polar solvent.