A method for statement shifting to increase the parallelism of loops includes constructing a data dependence graph (DDG) to represent dependences between statements in a loop, constructing a basic equations group from the DDG, constructing a dependence equations group derived in part from the basic equations group, and determining a shifting vector for the loop from the dependence equations group, wherein the shifting vector to represent an offset to apply to each statement in the loop for statement shifting. Other embodiments are also disclosed.