The magnetohydrodynamic (MHD) normal modes of oscillation of sheared coronal arcades including longitudinal wave propagation are studied. Solutions have been computed to ascertain the effects of the longitudinal magnetic field component, By, and of the longitudinal wavenumber, ky, in these structures. Our results show that whenever By≠0 and/or ky≠0, fast modes, characterized by a global velocity structure and a discrete spectrum of frequencies, and Alfvén continuum modes, characterized by a velocity perturbation confined to given magnetic surfaces, get coupled and no pure fast modes or pure Alfvén modes exist, but modes with mixed properties arise. These oscillatory modes display a global spatial distribution, together with a nonsquare integrable singular behavior on certain magnetic surfaces. Moreover, this mode coupling is such that under some circumstances the Alfvénic contribution is also in the form of a smooth velocity profile covering a range of magnetic surfaces instead of a singularity on a fixed magnetic surface. The coupling between fast and Alfvén modes is governed by the parity of their eigenfunctions in the direction along the equilibrium magnetic field. The parity rules determining the features of coupled modes in terms of their spatial structure, ky, and By are presented. We have found that the frequency of coupled modes is real when either By≠0 or ky≠0 but is complex when both By≠0 and ky≠0. Also, an important result is that coupled modes may not be observable since many of them leak energy away from the solar corona.