The Boolean satisfiability problem (SAT) has various applications in electronic design automation (EDA) fields such as testing, timing analysis and logic verification. SAT has been typically applied to EDA as follows: 1) formulation of the given problem as a SAT instance 2) solution of the SAT instance. In this paper, we present a method to simultaneously solve several closely related SAT instances using incremental satisfiability (ISAT). In ISAT, the decision sequence made for a ?prefix? function is used to solve another set of functions which have a number of new constraints (extensions) added to the prefix function. Our experiments show that we can achieve significant gains in total runtime when we use this methodology as opposed to resetting the decision sequences and solving each instance from scratch. Application of ISAT to delay fault testing is presented by formulating incremental path sensitization as an ISAT problem. Non-robust tests for the combinational portion of ISCAS 89 circuits are generated using this method.