A sensor is provided that includes a flexible wrap enclosure which is folded about the sensor. The flexible wrap includes primary flaps and at least one reinforcement flap. The reinforcement flap may be used to enclose areas of the sensor not enclosed by the primary wrap and/or may be used to provide reinforcement of the enclosure to prevent tearing of the flexible wrap enclosure. The sensor may be placed on a patient's finger, toe, ear, and so forth to obtain pulse oximetry or other physiological measurements.