An intra-oral mandibular advancement appliance to be inserted in the mouth of a patient so as to permit the position of the lower jaw of the patient to be adjusted relative to the upper jaw to maintain an airway to the throat through which the patient can breathe while sleeping, said appliance comprising: an upper tray assembly having an arcuate shape against which the teeth of the patient's upper jaw are seated, said upper tray assembly having a front and a pair of sides lying opposite and spaced from one another; a lower tray assembly having an arcuate shape against which the teeth of the patient's lower jaw are seated, said lower tray assembly also having a front and a pair of sides lying opposite and spaced from one another; characterized by a position adjustment block located at each of the pair of sides of said lower tray assembly; and a locking channel located at each of the pair of sides of said upper tray assembly and, each position adjustment block being slidably received within a respective locking channel, whereby said lower tray assembly is mated in releasable locking engagement to said upper tray assembly to prevent a displacement of said lower tray assembly relative to said upper tray assembly, wherein said lower tray assembly is responsive to a lateral compressive squeezing force simultaneously applied to the opposite sides thereof to temporarily change the shape of and deform said lower tray assembly to enable each position adjustment block to slide through its respective locking channel so as to release the locking engagement of said lower tray assembly to said upper tray assembly and thereby permit the positions of said lower tray assembly and the patient's lower jaw to be adjusted relative to the positions of said upper tray assembly and the patient's upper jaw. an upper tray assembly having an arcuate shape against which the teeth of the patient's upper jaw are seated, said upper tray assembly having a front and a pair of sides lying opposite and spaced from one another; a lower tray assembly having an arcuate shape against which the teeth of the patient's lower jaw are seated, said lower tray assembly also having a front and a pair of sides lying opposite and spaced from one another; characterized by a position adjustment block located at each of the pair of sides of said lower tray assembly; and a locking channel located at each of the pair of sides of said upper tray assembly and, each position adjustment block being slidably received within a respective locking channel, whereby said lower tray assembly is mated in releasable locking engagement to said upper tray assembly to prevent a displacement of said lower tray assembly relative to said upper tray assembly, wherein said lower tray assembly is responsive to a lateral compressive squeezing force simultaneously applied to the opposite sides thereof to temporarily change the shape of and deform said lower tray assembly to enable each position adjustment block to slide through its respective locking channel so as to release the locking engagement of said lower tray assembly to said upper tray assembly and thereby permit the positions of said lower tray assembly and the patient's lower jaw to be adjusted relative to the positions of said upper tray assembly and the patient's upper jaw.