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This paper proposes a three-layer model where, in each layer, an analytical expression is used for the speed of sound variation. This results in analytic, easily handled expressions for the ray paths. The speed of sound and its first derivative are matched at each layer interface; the depth of each layer is adjusted, dependent upon the experimental points. The upper layer is either a quadratic or cubic polynomial, the middle layer is a hyperbolic cosine, and the lower layer is linear. The model includes reflections from arbitrary analytic bottoms and flat ocean surfaces. The computer is used purely for computational results, not for integration. This theory may be considered as a 'zeroth'-order, analytical solution for more complex propagation models. [ABSTRACT FROM AUTHOR]