Some vacuum chambers in particle accelerators perform a waveguide- or resonator-like behavior due to their unique geometries. Electron multipacting caused by such a structural property might be able to overwhelm the classical beam-induced multipacting. This article shows that the wakefields of particle beams could stimulate the resonant modes of a vacuum chamber with a near-rectangular waveguide shape and accordingly induce much stronger electron avalanche in the chamber. Especially, it has been believed that the multipacting is responsible for pressure rise in a vacuum chamber, where energetic secondary electrons with growing numbers collide with gas particles at the chamber wall. Based on numerical simulations, the electron multipacting mechanism with the mode resonance is proposed, which can explain the significant pressure variation measured in our cryogenic vacuum chamber.