Optimization of a rectangular profile annular fin with variable pipe inside radius is presented. This optimum procedure is based on fixed fin height and is made by using variables separation method. The optimum heat loss, corresponding optimum fin length and optimum fin efficiency are presented as a function of pipe inside radius, fin half height, inside fluid convection characteristic number and ambient convection characteristic number. One of results shows that the optimum fin length increases linearly with increase of pipe inside radius for fixed fin height and fin base radius.