This work was motivated by the goal of building a robot capable of swimming on a microscopic scale by changing its shape. Two approaches to low Reynolds number swimming are studied. A deformable sphere is investigated which uses a method of construction called tensegrity to allow changes in shape. We found a method of matching tensegrity spheres to desired shapes and investigated the use of shape memory alloy coils as tensile elements. We propose a model for a box-shaped deformable swimmer, and a prototype is built and tested. The negative results from the prototype tests are then investigated by measuring the drag forces caused by pushing different block sizes through high viscosity fluid. Based on our experimental results we validate our approach and recommend design modifications for a second generation robot