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 $sim 10^5R_odot$ ($7cdot 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.
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