In this work, we study two scenarios of the Universe filled by a perfect fluid following the traditional dark energy and a viscous fluid as dark matter. In this sense, we explore the most simple case for the viscosity in the Eckart formalism, a constant, and then, a polynomial function of the redshift. We constrain the phase-space of the model parameters by performing a Bayesian analysis based on Markov Chain Monte Carlo method and using the latest data of the Hubble parameter (OHD), Type Ia Supernovae (SNIa) and Strong Lensing Systems. The first two samples cover the region $$0.01<z<2.36$$ 0.01 < z < 2.36 . Based on AIC, we find equally support of these viscous models over Lambda-Cold Dark Matter (LCDM) taking into account OHD or SNIa. On the other hand, we reconstruct the cosmographic parameters (q, j, s, l) and find good agreement to LCDM within up to $$3\sigma $$ 3 σ CL. Additionally, we find that the cosmographic parameters and the acceleration-deceleration transition are sensible to the parameters related to the viscosity coefficient, making of the viscosity an interesting physical mechanism to modified them.