This paper presents an analytical solution for an infinite strip having a circular inclusion, when the strip is subjected to pressure on both sides of the strip. In the analysis, two types of inclusions, i.e., perfectly bonded inclusion (displacements and tractions are continuous) and slipping inclusion (tractions and normal displacements are continuous and shear traction vanishes) are discussed. The solution is based on the Papcovich-Neuber displacement potentials approach and is deduced through making use of simple forms of Cartesian and cylindrical harmonics. The boundary conditions on both sides of the strip and around the inclusion are fully satisfied with the aid of the relationships between the Cartesian and cylindrical harmonics. The solution is represented in the form of graphs and the effects of the inclusions on the stress distribution are clarified.