  A number of Type I (hydrogenless) superluminous supernova (SLSN) events have
been discovered recently. However, their nature remains debatable. One of the
most promising ideas is the shock-interaction mechanism, but only simplified
semi-analytical models have been applied so far. We simulate light curves for
several Type I SLSN (SLSN-I) models enshrouded by dense, non-hydrogen
circumstellar envelopes, using a multi-group radiation hydrodynamics code that
predicts not only bolometric, but also multicolor light curves. We demonstrate
that the bulk of SLSNe-I including those with relatively narrow light curves
like SN 2010gx or broad ones like PTF09cnd can be explained by the interaction
of the SN ejecta with he CS envelope, though the range of parameters for these
models is rather wide. Moderate explosion energy ($\sim (2 - 4)\cdot 10^{51}$
ergs) is sufficient to explain both narrow and broad SLSN-I light curves, but
ejected mass and envelope mass differ for those two cases. Only 5 to 10
$M_\odot$ of non-hydrogen material is needed to reproduce the light curve of SN
2010gx, while the best model for PTF09cnd is very massive: it contains almost $
50 M_\odot $ in the CS envelope and only $ 5 M_\odot $ in the ejecta. The CS
envelope for each case extends from 10 $R_\odot$ to $\sim 10^5R_\odot$ ($7\cdot
10^{15} $ cm), which is about an order of magnitude larger than typical
photospheric radii of standard SNe near the maximum light. We briefly discuss
possible ways to form such unusual envelopes.
