This paper addresses control problems for flexible robot arms by using direct strain feedback. The purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily. We concentrate on one-link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers. A key contribution of this paper is the introduction of the concept of (strict) A-dependent operators, which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in Hilbert spaces. Several control experiments are performed, verifying the main theoretical points of this paper, demonstrating satisfactory control results of direct strain feedback, and leading to potential application of this simple control method for flexible robot control.