We study the Casimir effect in the presence of an extradimension compactified on a circle of radius R (M-4 x S-1 spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell action into a massless sector containing the 4D Maxwell action and an extra mass less scalar field and a Proca sector containing 4D gauge fields with masses m(n) = n/R where n is a positive integer. An important point is that, in the presence of perfectly conducting parallel plates, the three degrees of freedom do not yield three discrete (non-penetrating) modes but two discrete modes and one continuum (penetrating) mode. The massless sector reproduces Casimir's original result and the Proca sector yields the corrections. The contribution from the Proca continuum mode is obtained within the frame work of Lifshitz theory for plane parallel dielectrics where as the discrete modes are calculated via 5D formulas for the piston geometry. An interesting manifestation of the extra compact dimension is that the Casimir force between perfectly conducting plates depends on the thicknesses of the slabs.