This report covers the theoretical analysis two normally intersecting cylindrical shells having rati's of radii p?/R not greater than one-third.Both shells are considered to be infinitely long, capped at the ends and subjected to internal pressure.The exact solution of the partial differential equation of Donnells theory of thin cylindrical shells is obtained in the form of infinite series. Fourier expansions and the method of least square error are employed to satisfy the boundary conditions.Various numerical results are presented at the end of the report.