Laminated composites are one of the evolving materials in the field of civil engineering construction materials. The main focus of this study is to perform free vibrational analysis of laminated composite conoidal shells. The formulation is done using six node linear strain triangle elements. Finite element coding is done using ForTran to form the global stiffness matrix and global mass matrix. The non-dimensional fundamental frequencies and corresponding mode shapes are determined using Matlab®. Several problem cases with different boundary conditions, varying the geometry curvature ratios' and several types of laminae were used to conduct this study. The results are then compared with those given in the literature. The non-dimensional fundamental frequencies obtained using six node linear strain triangle element are in good agreement with those given in the literature using eight node quadrilateral elements. The fundamental frequency increases with the increase in the number of constraints and the case of lamina 45/-45/45/-45 gave the highest frequency for most of the boundary conditions.