The motivation of this paper is to investigate two viscous fluid cosmo
logical models in General Relativity in which the expansion is only in
two directions i.e. one of the Hubble parameters (H-1 = A(4)/A) is ze
ro. In the first model, coefficient of shear viscosity is assumed to b
e constant while In the second model, the coefficient of shear viscosi
ty is proportional to the rate of expansion in the model. Here no addi
tional condition is assumed except for coefficient of shear viscosity.
These models are new and different from those models obtained by Ball
and Jain (1987, 1988) in which free gravitational held was assumed to
be Petrov Type D and non-degenerate for Marder (1958) metric and coef
ficient of shear viscosity is proportional to the rate of expansion in
the model. The various physical and geometrical aspects of the models
are also discussed.