Reel-lay process is considered the most efficient installation/construction methods for offshore pipelines and has attracted particular interest on the designing of pipe with large elastic deformation capacity. Therefore, an unbonded, flexible composite ball joints pipe is proposed. The pipe is comprising an internal composite pipe segment with its ball joining to play as liner i.e., carcass, and one or more helical wounding tape stacks applied to the internal liner for absorbing axial and bending loads. The composite tape stacks are formed from a plurality of thin tape strips. All the layers are manufactured from a lightweight composite material consisting of highly noncorrosive epoxied matrix reinforced by long continuous fibers. This paper describes the design parameters of the pipe segments (e.g., modeled as laminated composite cylindrical shell) that form the pipe and its elastic deformations capacity under pure bending conditions (e.g., typical reeling installation condition). To this aim, a straightforward treatment of the problem is presented via using Hamilton's principle and based on the first order shear deformation theories. The solution of the laminated composite cylindrical shell was formulated to follow exactly a simply supported boundary condition. The inter-laminar stresses are evaluated for wide range of orthotropy ratio. Copyright 2013, Offshore Technology Conference.