Biologically inspired design (BID) is a widespread and growing movement in modern design, pulled in part by the need for environmentally sustainable design and pushed partly by rapid advances in biology and the desire for creativity and innovation in design. Yet, our current understanding of cognition in BID is limited and at present there are few computational methods or tools available for supporting its practice. In this dissertation, I develop a cognitive model of BID, build computational methods and tools for supporting its practice, and describe results from deploying the methods and the tools in a Georgia Tech BID class. One key and novel finding in my cognitive study of BID is the surprisingly large degree to which biological analogues influence problem formulation and understanding in addition to generation of design solutions. I call the process by which a biological analogue influences the evolution of the problem formulation analogical problem evolution. I use the method of grounded theory to develop a knowledge schema called SR.BID (for structured representations for biologically inspired design) for representing design problem formulations. I show through case study analysis that SR.BID provides a useful analytic framework for understanding the two-way interaction between problems and solutions. I then develop two tools based on the SR.BID schema to scaffold the processes of problem formulation and analogue evaluation in BID. I deployed the two tools, the four-box method of problem specification and the T-chart method of analogical evaluation, in a Georgia Tech BID class. I show that with minimal training, the four-box method was used by students to complete design problem specifications in 2011 and 2012 with 75% of students achieving better than 80% accuracy. Finally I describe a web-based application for interactively supporting BID practice including problem formulation and analogue evaluation. Thus, my dissertation develops a cognitive model of analogical problem evolution in BID, a knowledge schema for representing problem formulations, a computational technique for evaluating biological analogues, and an interactive web-based tool for supporting BID practice. Through a better cognitive understanding of BID and computational methods and tools for supporting its practice, it also contributes to computational creativity.