A downhole power generator has a substantially tubular body. A cover surrounds at least a portion of the body. At least one piezoelectric element is disposed in a cavity in the body, the piezoelectric element acting cooperatively with the cover such that motion of the cover relative to the body causes the piezoelectric element to generate electric power. A method for generating power downhole comprises disposing a cover around at least a portion of a substantially tubular body; disposing at least one piezoelectric element in the body; and engaging the piezoelectric element with the cover such that motion of the cover relative to the body causes the piezoelectric element to generate electric power.