Trace analysis for a security protocol represents every possible run as a trace and analyzes whether any insecure run is reachable. The number of traces will be infinite due to (1) infinitely many sessions of a protocol, (2) infinitely many principals in the network, and (3) infinitely many messages that intruders can generate. This paper presents an on-the-fly model checking method by restricting/abstracting these infinite factors to a finite model. First, we restrict a typed process calculus to avoid recursive operations, so that only finitely many sessions are considered. Next, a bound variable is introduced as an index of a message to represent its intended destination, so that an unbounded number of principals are finitely described. Then, messages in which irrelevant parts are reduced in a protocol are unified to a parametric message based on the type information. We implement the on-the-fly model checking method using Maude, and automatically detect the flaws of several security protocols, such as the NSPK protocol and the Woo-Lam protocol, etc..