  We investigate the possibility of testing cosmological models with
interaction between matter and energy sector. We assume the standard FRW model
while the so called energy conservation condition is interpreted locally in
terms of energy transfer. We analyze two forms of dark energy sectors: the
cosmological constant and phantom field. We find a simple exact solution of the
models in which energy transfer is described by a Cardassian like term in the
relation of $H^{2}(z)$, where $H$ is Hubble's function and $z$ is redshift. The
considered models have two additional parameters $(\Omega_{\text{int}},n)$
(apart the parameters of the $\Lambda$CDM model) which can be tested using SNIa
data. In the estimation of the model parameters Riess et al.'s sample is used.
We also confront the quality of statistical fits for both the $\Lambda$CDM
model and the interacting models with the help of the Akaike and Bayesian
informative criteria. Our conclusion from standard best fit method is that the
interacting models explains the acceleration of the Universe better but they
give rise to a universe with high matter density. However, using the tools of
information criteria we find that the two new parameters play an insufficient
role in improving the fit to SNIa data and the standard $\Lambda$CDM model is
still preferred. We conclude that high precision detection of high redshift
supernovae could supply data capable of justifying adoption of new parameters.
