  We study the effect of anisotropic escape mechanism on elliptic flow in
relativistic heavy-ion collisions. We use Glauber model to generate initial
conditions and ignore hydrodynamic expansion in the transverse direction. We
employ Beer-Lambert law to allow for the transmittance of produced hadrons in
the medium and calculate the anisotropy generated due to the suppression of
particles traversing through the medium. In order to separate non-flow
contribution due to surface bias effects, we ignore hydrodynamic expansion in
the transverse direction and consider purely longitudinal boost-invariant
expansion. We calculate the transverse momentum dependence of elliptic flow,
generated from anisotropic escape mechanism due to surface bias effects, for
various centralities in $\sqrt{s_{NN}}=200$ GeV Au$+$Au collisions at RHIC and
$\sqrt{s_{NN}}=2.76$ TeV Pb$+$Pb collisions at LHC. We find that the surface
bias effects have a sizable contribution to the total elliptic flow observed in
heavy-ion collisions indicating that the viscosity of the QCD matter extracted
from hydrodynamic simulations may be underestimated.
