Abstract By using point-matching approach under the weak guidance approximation, the dispersion curves of a dielectric light guide, with a new unconventional cross-section of plano-concave lens shape, are investigated. The suggested structure may be conceived as a distortion of the square with transverse compression at its one side. A comparison is made between the dispersion curves of the proposed and square waveguides. It is noticed that the lowest cutoff value (Vc) for the proposed waveguide is increased as compared to a square waveguide, and it supports more modes than the square waveguide at a particular value of normalized frequency V. Subsequently, the cutoff V-values are crowded within small range V=2.9–5.4, which is considered as an important feature of such plano-concave light guide. The obtained results are compared and interpreted with those already reported for biconcave lens shaped waveguides. Hence, this paper also reports the tolerance behavior of a square waveguide into concave lens shapes.