A 3 X 2 optical fiber flat coupler can be made by fusion and elongation of three adjacent fibers. Two types of resonant structure can be formed by leading back one of the output ports to one of the input ports. They are called symmetrical and asymmetrical ring resonators. The study is limited to the symmetrical case assuming low coupling coefficients. The output signals are very sensitive to the input wavelength and the length of the fiber ring. In this work, two cases are studied. In case A, the light launched to one of the input ports results in two in-phase output signals, while the light launched to other input port results in two out of phase output signals. In case B, there is a complete switching of power from one output port to the other.