This paper deals with the problems of asymptotic stability, exponentially stability and admissibility for a mathematical model of singular systems with constant delay. First, the singular system is transformed into a neutral differential system. Secondly, some sufficient conditions are obtained on the stability and the admissibility of solutions of the new neutral differential system using integral inequalities, linear matrix inequality (LMI) technique and meaningful Lyapunov-Krasovskii functionals. At the end, two numerical examples are given to show the effectiveness and applicability of the proposed method and the obtained results. These results generalize the existing ones.