[en] A formulation of the continuum random-phase approximation (CRPA) equations with a finite-range particle-hole (ph) interaction is presented. The resulting equations can be applied to the calculation of RPA wave functions not only in the continuum, but also in the bound region. These CRPA equations, which are inhomogeneous coupled-channel integro-differential equations with a large dimension and thus difficult to solve, are modified so that the Lanczos method can be applied to solve them relatively easily. As examples we apply our method to the 3^- bound state and the giant quadrupole resonance (GQR) in ¹⁶O and ⁴⁰ Ca. A nuclear matter G-matrix is used for the ph interaction. Since treating the continuum exactly introduces in effect an infinitely large shell-model space, the ph correlations induced by the G-matrix interaction are too strong, not only for the bound collective states but also for collective states in the continuum. Renormalizing the exchange ph matrix elements allows one to fit the experimental data in both the bound and continuum part of the excitation spectrum in a consistent manner. For both the low-lying and continuum region the ring approximation is shown to be a good approximation for dealing with the exchange part of the ph matrix elements that are responsible for the ground-state correlations. (orig.)