  We use the Szekeres inhomogeneous relativistic models in order to fit
supernova combined data sets. We show that with a choice of the spatial
curvature function that is guided by current observations, the models fit the
supernova data almost as well as the LCDM model without requiring a dark energy
component. The Szekeres models were originally derived as an exact solution to
Einstein's equations with a general metric that has no symmetries and are
regarded as good candidates to model the true lumpy universe that we observe.
The null geodesics in these models are not radial. The best fit model found is
also consistent with the requirement of spatial flatness at CMB scales. The
first results presented here seem to encourage further investigations of
apparent acceleration using various inhomogeneous models and other constraints
from CMB and large structure need to be explored next.
