Abstract <p> When quantizing field-theoretical models with gauge symmetries, quantum anomalies are often encountered. It is commonly believed that the cause of these anomalies lies in the infinite numbers of degrees of freedom, which requires the field system to be completed within a suitable regularization and renormalization scheme. We present an example of a finite-dimensional Hamiltonian system with first-class constraints, whose quantization leads to unavoidable quantum anomalies. These anomalies arise due to the nontrivial topology of the reduced phase space of the system. </p>