Minimally invasive surgery (MIS) has several advantages over traditional methods. Scaling MIS instruments to smaller sizes and increasing their performance will enable surgeons to offer new procedures to a wider range of patients. In this work, two compliant mechanism-based minimally invasive surgical instrument wrist or gripper mechanisms are designed and analyzed.The cylindrical cross-axis flexural pivot (CCAFP) is a single-degree-of-freedom wrist mechanism that could be combined with existing gripper mechanisms to create a multi-degree-of freedom instrument. The simplicity of the CCAFP mechanism facilitates analysis and implementation. The flexures of the CCAFP are integral with the instrument shaft, enabling accessories to be passed through the lumen. The CCAFP is analyzed and determined to be a viable wrist mechanism for MIS instruments based on research results. A finite element (FE) model of the mechanism is created to analyze the force-deflection and strain-deflection relationships. Experimental results are used to verify the FE model. A 3 mm design is created that could undergo an angular deflection of +/- 90 degrees. The addition of cam surfaces to help guide the flexures and limit the maximum stress during deflection is explored. These cam surfaces can be integral to the instrument shaft along with the flexures. A 2 degree-of-freedom (DoF) CCAFP with intersecting axes of rotation is also introduced. The inverted L-Arm gripper compliant mechanism has 2 DoF, one wrist and one gripping. Three challenges associated with using compliant mechanisms in MIS instruments are considered: inadequate performance in compression, large flexure deformations, and a highly variable mechanical advantage. These challenges were resolved in the L-Arm design by inverting the flexures, tailoring flexure geometry and employing nitinol, and integrating pulleys into each jaw of the mechanism. The L-Arm was prototyped at several sizes to demonstrate functionality and scalability. A finite element model of the L-Arm flexure was created to determine the strain-deflection relationship. A fatigue test was completed to characterize nitinol for use in compliant mechanism MIS instruments.These concepts demonstrate the ability of compliant mechanisms to overcome the design and manufacturing challenges associated with MIS instruments at the 3 mm scale. The models and principles included in this work could be used in the application of compliant mechanisms to design new MIS instruments as well as in other areas that employ compliant mechanisms in a cylindrical form factor.