The minimum volume of nonlinear longitudinal fin with rectangular and triangular profile by using the modified Newton-Raphson method is present in this paper. The dimension of the fin profile is regarded as optimization variables. Furthermore, a mechanism called “volume updating” is added into the modified Newton-Raphson algorithm to obtain the minimum volume of the fin. Two examples are illustrated to demonstrate the proposed method. The obtained results showed that the proposed method use efficiently and accurately in finding the minimum volume of the nonlinear longitudinal fin problem with the rectangular and triangle profile.