With the aim of producing innovative clutch actuation mechanisms for automotive transmissions, we are investigating a design based on power screws. The design strives to improve clutch actuation technology and minimize energy consumption by maintaining clutch lock-up independent of an external energy source. The system consists of a lead screw shaft-and-nut assembly, a clutch apply-plate, a set of wet clutch disks and a brushless DC motor. The clutch actuation assembly is separated from the clutch-pack via thrust bearings, which allows the use of a motor, while reducing the inertial load imposed by the conventional clutch-pack. A prototype of the design was fabricated and installed on a testbed, to mimic the installation of the actuator to replace the hydraulic components. A standard 12-disk clutch-pack of an automatic transmission was used within the apparatus. The formulation of the mathematical model of the entire testbed is described in this paper. The clutch-pack stiffness is modeled as a hardening spring, to account for its elastostatic behavior. The simulated response of the model was compared to its experimental counterpart, which allowed for a rough estimate of the model parameters. Compressive force testing of the apparatus using a load cell is included.