  A class of Stephani cosmological models as a prototype of non-homogeneous
universe is considered. The non-homogeneity can lead to accelerated evolution
which is now observed from the SNIa data. Three samples of type Ia supernovae
obtained by Perlmutter at al., Tonry et al. and Knop et al. are taken into
account. Different statistical methods (best fits as well as maximum likelihood
method) to obtain estimates of the model parameters are used. Stephani model is
considered as an alternative to the concordance of Lambda-CDM model in the
explanation of the present acceleration of the universe. The model explains the
acceleration of the universe at the same level of accuracy as the Lambda-CDM
model. From the best fit analysis it follows that the Stephani model is
characterized by higher value of nonrelativistic matter density parameter than
the Lambda-CDM model. It is also shown that the obtained results are consistent
with location of CMB peaks.
