Electrostatic transducers are usually operated under a DC bias below their collapse voltage. The same scheme has been adopted for capacitive micromachined ultrasonic transducers (cMUTs). DC bias deflects the cMUT membranes toward the substrate, so that their centers are free to move during both receive and transmit operations. In this paper, we present time-domain, finite element calculations for cMUTs using LS-DYNA, a commercially available finite element package. In addition to this DC bias mode, other new cMUT operations (collapse and collapse-snapback) have recently been demonstrated. Because cMUT membranes make contact with the substrate in these new operations, modeling of these cMUTs should include contact analysis. Our model was a cMUT transducer consisting of many hexagonal membranes; because it was symmetrical, we modeled only one-sixth of a hexagonal cell loaded with a fluid medium. The finite element results for both conventional and collapse modes were compared to measurements made by an optical interferometer; a good match was observed. Thus, the model is useful for designing cMUTs that operate in regimes where membranes make contact with the substrate.