Peridynamic theory is the reformulation of classical mechanics mathematical theory compatible with cracks while performing structural analysis. The present study models the tubular joints having T, Y, K, and X configurations in the peridynamic framework by implementing peridynamic shell governing equations. The linear response of the structure is validated by comparing the magnitude of deformations under static loading and the displacement variation at the subsequent load steps varying in a sinusoidal and irregular manner with the abaqus results. The crack initiation location at the stress-concentrated region and the crack growth path leading to fracture under linearly increasing loads for the considered tubular joints can be inferred from this approach. A comparative study is performed among the joint configurations based on the linear displacement variation and critical loads for the unstable deformation due to damaged material points at the joint intersection. In the present paper, apart from validating the implementation of novel theory in the offshore structure, the drawbacks and intricacies of the classical approach for studying crack initiation and growth in complex tubular joint structures are resolved by the peridynamic approach.