In multiprocessors, memory models are introduced to describe the executions of programs among processors. Relaxed memory models, which relax the order of executions, are used in the most of the modern processors, such as ARM and POWER. Due to a relaxed memory model could change the program semantics, the executions of the programs might not be the same as our expectation that should preserve the program correctness. In addition to relaxed memory models, the way to execute an instruction is described by an instruction semantics, which varies among processor architectures. Dealing with instruction semantics among a variety of assembly programs is a challenge for program verification. Thus, this paper proposes a way to verify a variety of assembly programs that are executed under a relaxed memory model. The variety of assembly programs can be abstracted as the way to execute the programs by introducing an operation structure. Besides, there are existing frameworks for modeling relaxed memory models, which can realize program executions to be verified with a program property. Our work adopts an SMT solver to automatically reveal the program executions under a memory model and verify whether the executions violate the program property or not. If there is any execution from the solver, the program correctness is not preserved under the relaxed memory model. To verify programs, an experimental tool was developed to encode the given programs for a memory model into a first-order formula that violates the program correctness. The tool adopts a modeling framework to encode the programs into a formula for the SMT solver. The solver then automatically finds a valuation that satisfies the formula. In our experiments, two encoding methods were implemented based on two modeling frameworks. The valuations resulted by the solver can be considered as the bugs occurring in the original programs.