We propose and investigate integrated metal-dielectric-metal (MDM) resonators operating with semi-guided waves (guided modes of dielectric slab waveguides). The MDM resonators are constituted by two metal strips "buried" in the waveguide core layer and separated by a dielectric waveguide segment. We theoretically prove and numerically demonstrate that by a proper choice of the mode incidence geometry, the widths of the metal strips, and the distance between them, it is possible to achieve either total absorption of the incident wave or coherent perfect absorption (in the case of symmetric incidence of two modes on the structure). The proposed planar MDM resonators may find application as absorbers or filters in integrated optical circuits.