  We develop a model of coronal-loop oscillations that treats the observed
bright loops as an integral part of a larger 3-D magnetic structure comprised
of the entire magnetic arcade. We demonstrate that magnetic arcades within the
solar corona can trap MHD fast waves in a 3-D waveguide. This is accomplished
through the construction of a cylindrically symmetric model of a magnetic
arcade with a potential magnetic field. For a magnetically dominated plasma, we
derive a governing equation for MHD fast waves and from this equation we show
that the magnetic arcade forms a 3-D waveguide if the Alfv\'en speed increases
monotonically beyond a fiducial radius. Both magnetic pressure and tension act
as restoring forces, instead of just tension as is generally assumed in 1-D
models. Since magnetic pressure plays an important role, the eigenmodes involve
propagation both parallel and transverse to the magnetic field. Using an
analytic solution, we derive the specific eigenfrequencies and eigenfunctions
for an arcade possessing a discontinuous density profile. The discontinuity
separates a diffuse cylindrical cavity and an overlying shell of denser plasma
that corresponds to the bright loops. We emphasize that all of the
eigenfunctions have a discontinuous axial velocity at the density interface;
hence, the interface can give rise to the Kelvin-Helmholtz instability.
Further, we find that all modes have elliptical polarization with the degree of
polarization changing with height. However, depending on the line of sight,
only one polarization may be clearly visible.
