  In this paper we have considered a flat FLRW universe with bulk viscous
Zel'dovich as the cosmic component. Being considered the bulk viscosity as per
the Eckart formalism, we have analyzed the evolution of the Hubble parameter
and constrained the model with the Type Ia Supernovae data thus extracting the
constant bulk viscous parameter and present Hubble parameter. Further we have
analyzed the scale factor, equation of state and deceleration parameter. The
model predicts the late time acceleration and is also compatible with the age
of the universe as given by the oldest globular clusters. We have also studied
the phase-space behavior of the model and found that a universe dominated by
bulk viscous Zel'dovich fluid is stable. But on the inclusion of radiation
component in addition to the Zel'dovich fluid, makes the model unstable. Hence,
even though the bulk viscous Zel'dovich fluid dominated universe is a feasible
one, the model as such failed to predict a prior radiation dominated phase.
