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We present the mathematical model, the computational algorithm, and the computer program in Visual Basic developed for the analysis of the optical-fiber refractometric transducer composed of the transparent dielectric detection element and two connecting optical fibers. The developed software performs the numerical ray-tracing of light propagation in the transducer. It allows one to calculate the optical transmission in the transducer as a function of the refractive index of the surrounding medium. The software allows one to analyze the detection elements having a smooth working surface of the second order of any of the following shapes: a segment of a sphere, ellipsoid, and paraboloid. Our results generalize previous work [1], [2] where the element geometry was a hemisphere. We validate our software with known analytical solutions.