In order to control the process of data mining and focus on the things of interest to us, many kinds of constraints have been added into the algorithms of data mining. However, discovering the correlated alarms in the alarm database needs deep domain constraints. Because the correlated alarms greatly depend on the logical and physical architecture of networks. Thus we use the network model as the constraints of algorithms, including Scope constraint, Inter-correlated constraint and Intra-correlated constraint, in our proposed algorithm called SMC (Search with Model-based Constraints). The experiments show that the SMC algorithm with Inter-correlated or Intra-correlated constraint is about two times faster than the algorithm with no constraints.