In the present paper, the effects of viscous dark matter are analysed \vithin the ACDM model. Here we consider bulk viscosity through the Israel-Stewart theory approach, leading to an effective pressure term in the continuity equation that accomplishes for the dissipative effects of the dark matter fluid. Then, the corresponding equation for viscosity is solved and a general equation for the Hubble parameter is obtained with the presence of a cosmological constant. The existence of de Sitter solutions is discussed, where a wider range of solutions is found in comparison to the ACDM model. Also the conditions for the near thermodynamical equilibrium of the fluid is analysed. Finally, a qualitative analysis provides some constraints on the model by using Supernovae la data which reveals the possible importance of causal thermodynamics in cosmology.