  We develop a formalism, based on the mode expansion method, to describe the
guided resonances and bound states in the continuum (BICs) in photonic crystal
slabs with one-dimensional periodicity. This approach provides analytic
insights to the formation mechanisms of these states: the guided resonances
arise from the transverse Fabry-P\'erot condition, and the divergence of the
resonance lifetimes at the BICs is explained by a destructive interference of
radiation from different propagating components inside the slab. We show BICs
at the center and on the edge of the Brillouin zone protected by symmetry, as
well as BICs at generic wave vectors not protected by symmetry.
