This paper studies characteristics of optimal airship flight trajectories in the atmosphere. Principles of airship flight are first reviewed. A three-dimensional point-mass model including the effect of added mass is developed. Airship flight from given initial conditions to specified final conditions is formulated as a nonlinear optimal control problem. Performances are selected to minimize the flight time or the energy consumption. Path constraints are imposed on airship states and controls in obtaining optimal flight trajectories. Approximate analytical solutions are obtained under several simplifying assumptions. Then, the original problem is converted into a parameter optimization problem using a collocation approach, and example numerical solutions are obtained. Main features of the numerical solutions are consistent with approximate analytical solutions. The flight times and energy consumptions of the two performance indices are compared.