Propeller optimization by means of calculus of variations is addressed in this paper. A procedure for deriving the Euler-Lagrange equations for both unconstrained and constrained propeller blade twist optimization is presented. This same procedure can be followed in order to optimize other geometric parameters, but blade twist is considered here in order to investigate the feasibility of a variable twist propeller blade. Results from unconstrained twist optimization show that regardless of the operating condition (takeoff, climb, or cruise) the maximum efficiency occurs at significantly lower power coefficients than what a propeller will be required to absorb. Constrained optimization supports this observation by showing that for each operating condition a power constraint lowers the propeller efficiency. Twist distributions obtained from constrained optimization for each of the three operating conditions differ significantly from one another, but it is shown that the effect on performance is insignificant. This leads to the conclusion that a variable twist propeller is not viable for a typical aircraft mission. For the case of a loiter-dash type mission profile, however, analysis shows that a variable twist propeller blade is indeed feasible.