In this paper, we present parallel implementations of the sparse Cholesky factorization kernel in the SPLASH-2 programs to evaluate performance of a Pentium Pro based SMP cluster. Solaris threads and remote memory operations are utilized for intranode parallelism and internode communications, respectively. Sparse Cholesky factorization is a typical irregular application with a high communication to computation ratio and no global synchronization between steps. We efficiently parallelized using asynchronous message handling instead of lock-based mutual exclusion between nodes, because synchronization between nodes reduces the performance significantly. We also found that the mapping of processes to processors on an SMP cluster affects the performance especially when the communication latency can not be hidden.