Optimization of the asymmetric trapezoidal fin with various upper lateral surface slope is made using a two-dimensional analytic method. For the fixed fin base height, the optimum heat loss, fin length and effectiveness are represented as inner fluid convection characteristic number, fin base thickness, fin base height, fin shape factor and ambient convection characteristic number. For this optimum procedure, the optimum heat loss is defined as 95% of the maximum heat loss from the fin. One of the results shows that optimum heat loss and effectiveness seems independent of the fin shape factor while optimum fin length decreases almost linearly as the fin shape factor increases.