The effect of incident field refraction on the scattered field from vertically extended cylindrical targets is investigated. A theoretical model for the total scattered field from a cylindrical target in a range-dependent ocean waveguide is developed from Green's theorem. The locally scattered field on the target surface is estimated as a function of the incident field by applying the appropriate boundary conditions on continuity of acoustic pressure and normal velocity, making the model applicable to general penetrable cylinders. The model can account for depth dependence in medium sound speed and hence refraction in the incident field along the target depth. Numerical implementation is done for a passive acoustic reflector, a long cylindrical air-filled rubber hose, often deployed vertically in experiments to provide calibration and charting consistency for wide-area active sonar systems. Analysis with the model indicates that refraction in the incident field along the target depth must be taken into account to accurately estimate the scattered field level from vertically extended cylindrical targets. It is demonstrated that the standard Ingenito waveguide target scattering model, which assumes that the incident field is planar along the target extent, can lead to significant errors of 10 dB or more in estimating the scattered field level.