A process that converts polymers (e.g., waste polyolefins) into useful mixtures of hydrocarbons using supported metal catalysts (i.e., transition metal catalysts supported on carbon or metal oxides). The polymers are solubilized in mixtures of organic compounds that are subjected to corresponding supercritical conditions. Two examples are described in the following. 1) Polymer and a stream of light hydrocarbons are contacted in a mixer to dissolve the polymer in a liquid phase. The stream with dissolved polymer is mixed with hydrogen and introduced to a fixed bed reactor containing the supported metal catalyst. The mixing step and the reactor are held, at least, at the temperature and pressure needed to reach supercriticality of the mixture of hydrocarbons dissolving the polymer. The effluent of the reactor is separated in two stages. The first one recovers hydrogen and gas products, whereas the second stage produces the stream of light hydrocarbons to dissolve the polymer and the stream of liquid products in the initial stage of the process. 2) Polymer is introduced, via an extruder, to a reactor containing a slurry of the supported catalyst. Hydrogen is also feed into the reactor. The pressure and temperature in this reactor are chose to keep the supercriticality of the liquid inside the reactor. The gas phase, which contains unreacted hydrogen and gas products, is extracted from the reactor and treated to recover hydrogen. The liquid/supercritical phase leaves the reactor for a separation step that separates the liquid products from the light products that are cycled back to the slurry reactor. In both cases polyolefins are converted to alkanes according to the following general reactions: (C2H4)m + xH2 → x(CnH2n+2) (C3H6)m + xH2 → x(CnH2n+2)