Continuous layer jamming is an effective tunable stiffness mechanism that utilizes vacuum to vary friction between laminates enclosed in a membrane. In this paper, we present a discrete layer jamming mechanism that is composed of a multilayered beam and multiple variable pressure clamps placed discretely along the beam; system stiffness can be varied by changing the pressure applied by the clamps. In comparison to continuous layer jamming, discrete layer jamming is simpler as it can be implemented with dynamic variable pressure actuators for faster control, better portability, and no sealing issues due to no need for an air supply. Design and experiments show that discrete layer jamming can be used for a variable stiffness co-robot arm. The concept is validated by quasi-static cantilever bending experiments. The measurements show that clamping 10% of the beam area with two clamps increases the bending stiffness by around 17 times when increasing the clamping pressure from 0 to 3 MPa. Computational case studies using finite element analysis for the five key parameters are presented, including clamp location, clamp width, number of laminates, friction coefficient, and number of clamps. Clamp location, number of clamps, and number of laminates are found to be most useful for optimizing a discrete layer jamming design. Actuation requirements for a variable pressure clamp are presented based on results from laminate beam compression tests.