The main purpose of this study was to develop a model for calculating forces produced by a swimmer’s hand, with the thumb adducted, accelerating in the direction of flow. The model included coefficients to account for the velocity and acceleration of the hand. These coefficients were designed to calculate forces in the direction opposite the motion (drag) and two components of lift orthogonal to the direction of motion. To determine the coefficients, three-dimensional forces acting on a resin cast of a swimmer’s hand were recorded while accelerating the hand from rest to 0.45 m · s⁻¹ and 0.6 m · ⁻¹ in a towing tank. The hand orientation was varied throughout the entire range at 5° increments. Three-dimensional surfaces describing the magnitude of the coefficients as functions of pitch and sweepback angle were produced. It was found that acceleration coefficients as well as velocity coefficients are required for accurate modeling of the forces produced by the hand in swimming. The forces generated by the hand are greatest when pitch angles approach 90° due to the large contribution by the drag component. However, at pitch angles near 45° and sweepback angles near 45° and 135°, lift forces contribute substantially.