Is it the stress that produces strain or strain produces stress?

A Force applied to an object will cause a displacement. Strain is effectively a measure of this displacement (change in length divided by original length). Stress is the Force applied divided by the area it is applied to. (eg. pounds per square inch) So, to answer the question, it is the applied Force that produces both stress and strain. Stress and strain are linked together by various material properties such as Poisson's ratio and Young's Modulus.