A new method based on Maxwell's equations, ABCD ray matrices, and total internal reflection is proposed to theoretically analyze the characteristics of eigenmodes confined in nano-width rectangle resonators. Using this method, mode wavelengths and indices of transverse and longitudinal modes are obtained. Another method based on the finite difference time domain technique and Pad′e approximation is used to numerically calculate resonant wavelengths, mode field distributions and quality factors. The results of two methods show that the resonant wavelengths obtained from both methods are very close, and the maximum relative error is less than 2%. The mode indices of transverse and longitudinal modes obtained agree well with mode field distribution patterns calculated by finite difference time domain techniques.