This paper proposes a computational model of the practical cognitive processes involved in insightful human problem solving. The solutions to insight problems require a drastic shift from an ‘impasse’ stage to the ‘insight’ stage. The impasse stage frequently experienced with insight problems is generally assumed to reflect special ‘constraints’ on the solver. It is also generally assumed that three mechanisms are necessary in order to escape from impasses: a mechanism to avoid failed trials, a chaotic mechanism, and a goal-orienting mechanism. The proposed model involves a system of simultaneous differential equations with each variable denoting a node in a neural network model. Constraints are modeled in terms of controls on the easiness with which the nodes are activated. The system has two special terms; one is a chaotic function representing the chaotic mechanism, and the second guides the system in the direction that maximizes an evaluation function value in representing the avoidance of failed trials. Through the representation of the goal-orienting mechanism, the model selects an operator that minimizes the difference between the current state and the goal state. Simulation results demonstrate that the model successfully models the cognitive processes of insightful problem solving, and provide evidence that all three mechanisms necessary for insight.