This thesis presents new models for determining piezoresistive response in long, thin polysilicon beams with either axial and bending moment inducing loads or torsional loads. Microelectromechanical (MEMS) test devices and calibration methods for finding the piezoresistive coefficients are also presented for both loading conditions. For axial and bending moment inducing loads, if the piezoresistive coefficients are known, the Improved Piezoresistive Flexure Model (IPFM) is used to find the new resistance of a beam under stress. The IPFM first discretizes the beam into small volumes represented by resistors. The stress that each of these volumes experiences is calculated, and the stress is used to change the resistance of the representative resistors according to a second-order piezoresistive equation. Once the resistance change in each resistor is calculated, they are combined in parallel and series to find the resistance change of the entire beam. If the piezoresitive coefficients are not initially known, data are first collected from a test device. Piezoresistive coefficients need to be estimated and the IPFM is run for the test device's different stress states giving resistance predictions. Optimization is done until changing the piezoresistive coefficients provides model predictions that accurately match experimental data. These piezoresistive coefficients can then be used to design and optimize other piezoresistive devices. A sensor is optimized using this method and is found to increase voltage response by an estimated 10 times. For torsional loads, the test device consists of a slider-crank connected to two torsional legs. The slider-crank creates torsional stress in the legs which causes a change in the electrical resistance through the legs. A model that predicts the effects of a scissor hinge on the slider-crank is presented. Torsional stresses in the legs are calculated delete{using the membrane analogy.} and the legs are discretized into long parallel resistors and the stresses delete{from the membrane analogy} applied to each resistor. Assuming a second-order piezoresistance, an optimization is then done to find the piezoresistive coefficients by changing them until the model prediction fits the test data. These coefficients can be used to predict angular displacement from resistance measurements in fully integrated torsional sensors. Potential applications are discussed, and a torsional accelerometer is presented.