It is challenging and important to establish reliability model for mechanical systems with multiple functional performances. This article develops a model of competing failure for mechanical systems under catastrophic failure due to external shocks and multi-functional failures. Shock model is used to analyze the catastrophic failure. Functional failures are demonstrated by functional indicators which are functions of specific variables including constant variables and degradation variables. Functional failure occurs if the functional indicators are beyond a limit δ. Brownian motion with non-linear drift is used to model the process of degradation variables. Besides, there are two kinds of dependence around these failure modes. The dependence of catastrophic failure and functional failure, due to shared external shock source, is illustrated by the instantaneous increments during degradation process; the dependence between multiple functional performances themselves is modeled by copula functions. Reliability of systems is calculated based on this model. A mechanical lock system is chosen as a case to verify the validity and practicability. This model can also be applied for other mechanical systems.