Explaining the causes of infeasibility of formulas has practical applications in various fields, such as formal verification and electronic design automation. A minimal unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. The problem of deriving minimal unsatisfiable cores from Boolean formulas has been addressed rather frequently in recent years. However little attention has been concentrated on extraction of unsatisfiable subformulas in Satisfiability Modulo Theories(SMT). In this paper, we propose a depth-first-search algorithm and a breadth-first-search algorithm to compute minimal unsatisfiable cores in SMT, adopting different searching strategy. We report and analyze experimental results obtaining from a very extensive test on SMT-LIB benchmarks.