In the present theory of elementary particles, it is usual to start from the quantized field, which is equivalent to the assembly of indefinite number of one sort of elementary particles. The field which should be quantized is sometimes the one wellknown in classical theory as in the case of the electromagnetic field, but it may have sometimes no direct counterpart in classical theory as in the case of the electron field, which appears first in quantum mechanics as the wave function or the probability amplitude. Hitherto it has been regarded, as one of the greatest success of relativistic quantum mechanics that the two thins, i.e. the material particle and the field of force, which had been entirely different from each other in classical theory as well as in nonrelativistic quantum mechanic, could be coordinated by the method of second quantization. If, however, we want to go into the problem of interaction between two sorts of elementary particles, we find at once the essential difference still remaining between field and matter. For instance, we consider usually the interaction between two electrons as due to intermediary action of the electromagnetic field instead of direct interaction at distance. In the very assumption of the coexistence of the field around the point particle lies the origin of the wellknown difficulties of the present theory. Although recent development of the meson theory of unclear forces seems to have made the situation more complicated because of the fact that the meson has been considered to be something with the dual nature, one of the main causes of newly added difficulties can still be ascribed to the point interaction between the nucleon and the meson field. Under these circumstances we can follow either of two ways of revision and completion the present theory particles. Namely, we can either pass over the difference between matter and field and devote ourselves to the establishment of the new scheme which may be applied to any kind of elementary particles, or we can first turn our attention to the difference of role played by field and matter and try to find the specified method of quantization appropriate for each of them, before we go into the construction of the general theory. Of course we cannot strictly distinguish between these two ways, but they are always mingled with each other in actual investigation. Nevertheless most of attempts hitherto made seem to lay stress on the revision of the method of quantization common to all sorts of elementary particles. In this paper, the author want to follow the latter way of discriminating field and matter in the beginning. Thus we can show that a natural extention of the field concept, which has been so useful in physics for many years since, leads to a generalized mixed field theory, and further to a suggestion for the new method of quantization of the material field.