**Introduction:**

For thick cylinders such as guns, pipes to hydraulic presses, high pressure hydraulic pipes the wall thickness is relatively large and the stress variation across the thickness is also significant.

**Description:**

The problem may be solved by considering an axisymmetry about z-axis and solving the differential equations of stress equilibrium in polar co-ordinates. In general the stress equations of equilibrium without body forces can be given as

For axisymmetry about z-axis and this gives

In a plane stress situation if the cylinder ends are free to expand σz = 0 and due to uniform radial deformation and symmetry

The equation of equilibrium reduces to

If we consider a general case with body forces such as centrifugal forces in the case of a rotating cylinder or disc then the equations reduce to

It is convenient to solve the general equation so that a variety of problems may be solved.