An analytical study of a waveguide with two parabolic cylindrical surfaces separating the guiding region of refractive indexn1from two cladding regions of common refractive indexn2withn1≳n2is presented. The cutoff conditions for modes are derived as equations containing trigonometric functions. The modes show a bunching tendency instead of well‐defined discreteness, and several mode bunches occur because the distance of separation between the two interfaces does not remain constant but continues to increase as one moves away from the region near the vertices of the parabolas. Unlike the planar waveguide, a nonzero cutoff is deduced which may be attributed to the curvature of the boundaries, and the flare.