This paper studies the symmetries and non-Noether conserved quantities of mechanical systems with unilateral non-Chetaev nonholonomic constraints. The differential equations of motion of the systems are established, and the definitions and criterions of Lie symmetry and Mei symmetry are given. For the unilateral non-Chetaev nonholonomic constraint system, it is proved that under some conditions a new conserved quantity called Hojman conserved quantity can be directly deduced from Lie symmetry, and a new conserved quantity called Mei conserved quantity can be directly deduced from Mei symmetry. The relations between the symmetries and the new conserved quantities are researched. At the end of the paper, an example is given to illustrate the application of the results.