Software error propagation is a crucial factor leading to software failures. Researchers study on the relationships between software structure measures and error propagation influences, aiming to guide software designing to mitigate the impact brought by error propagation behaviors. Unlike existing researches focusing on the number of nodes that involved in error propagation chains, this paper proposes a novel measure from the aspect of path deviation caused by error propagation, Error Execution Path Deviation (EEPD), to measure the influence of error propagation. It can measure the influences in multi-task systems more precisely because different paths in those systems normally represent different missions. We design fault injection experiments to collect the run-time data supporting the correlation study. The empirical study shows that there are strong relationships between several structure measures and EEPD. The results can assist in finding the error propagation critical nodes and guiding software design to reduce the impact on system caused by error propagation.