A model of MPI synchronization communication programs is presented and its three basic simplified models are also defined. A series of theorems and methods for deciding whether deadlocks will occur among the three models are given and proved strictly. These theories and methods for simple models' deadlock detection are the necessary base for real MPI program deadlock detection. The methods are based on a static analysis through programs and with runtime detection in necessary cases and they are able to determine before compiling whether it will be deadlocked for two of the three basic models. For another model, some deadlock cases can be found before compiling and others at runtime. Our theorems can be used to prove the correctness of currently popular MPI program deadlock detection algorithms. Our methods may decrease codes that those algorithms need to change to MPI source or profiling interface and may detects deadlocks ahead of program execution, thus the overheads can be reduced greatly.