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A flexible interferometry is proposed to test concave optical aspheric and free-form surfaces. It employs a flexible aberration generator (FAG) consisting of a movable reflective sphere (MRS) and two counter-rotating optical wedges (CROW). The FAG is able to generate low-order Zernike aberrations to compensate the inherent aberrations of the test surface by the rotation of wedges in CROW and translation (or tilt) of the MRS. For some surfaces with mild departure, the FAG would result in a resolvable interferogram by the different aberrations compensation and the flexible test is thus achieved. The practical calibration for FAG is also reported. After calibration, experiment results showing the validity of the flexible test are presented by testing an ellipsoidal mirror and an off-axis paraboloidal mirror. [ABSTRACT FROM AUTHOR]