Abstract: Thick-walled cylinder is widely used in practical engineerings. If the limit internal pressure is calculated accurately, it is great significance to prevent accidents and reduce risk. There are many engineering materials that the tensile strength and tensile modulus are different. These differences have a significant effect on the ultimate internal pressure. Previous studies have shown that only considering one aspect of the tension and compression strength and the modulus of tension and compression has a certain error with the actual situation. With consideration of the intermediate principal stress and the different elastic modulus and different strength in tension and compression, elastic and plastic stress distribution, the unified analytical solutions of the elastic limit internal pressure, the plastic limit internal pressure and the shakedown limit internal pressure of thick-walled cylinder under internal pressure are deduced based on twin shear unified strength theory. The correctness of the calculation results is proved through the verification and comparative analysis with other literatures. The influence of radius ratio, unified strength theory parameter, tension-compression ratio and coefficient of tensile-compression modulus of materials on the solutions is analyzed. It is shown that each unified solution increases with increasing the radius ratio and unified strength theory parameter but decreases with increasing the tensioncompression ratio. The elastic limit internal pressure decreases with increasing the coefficient of tension-compression modulus. When the wall thickness increases to a certain value, the shakedown limit internal pressure decreases with increasing the coefficient of tension-compression modulus. The different elastic modulus and strength in tension and compression have significant influence on the stability of the thick-walled cylinders. The consideration of the intermediate principal stress effect can make materials give full play to their potential. The variable law of the limit internal pressure with radius ratio provides reference for selecting reasonable wall thickness. The conclusion furnishes some theoretical basis for the engineering application of thick-walled cylinders.