A Hybrid Potential Flow (HPF) model for flow around a circular cylinder in the subcritical Reynolds number range (300 ≤ Re ≤ 3 × 105) is developed using a combination of elementary flow solutions and empirical data. By joining this developed near-body solution with von Karman's model for the vortex wake, a complete solution for flow around a circular cylinder is calculated. Results for oscillatory forces, including the transverse lift force, due to vortex shedding as well as shedding frequencies are then calculated and presented. With the complete solution for flow around a cylinder calculated, the HPF model can be used as a step to calculate the flow around other bluff bodies using conformal mapping, an approach that has been developed and presented by the authors in a related paper.