Non-edible cellulose-containing biomass is a promising and abundant feedstock for simple sugar production. This study presents the results of different cellulose-containing materials (CCM) hydrolysis experiments with P. verruculosum enzyme complexes in laboratory conditions. Among the non-pretreated substrates, only a few had a relatively high convertibility—soy bean husks (31%) and sugar beat pulp (20%)—while wheat straw, oat husks, sunflower peals, and corn stalks had a low convertibility of 3% to 12%. This indicates that a major part of CCM needs pretreatment. Steam-exploded (with Ca(OH)2) soy bean and oat husks (76% and 58%), fine ball-milled aspen wood and nitric acid-pretreated aspen wood (62% and 78%), and steam-exploded (with sulfuric acid) corn stalks (55%) had a high convertibility. Woody biomass pretreated with pulp and paper mills also had a high convertibility (56–78%)—e.g., never dried kraft hardwood and softwood pulp (both bleached and unbleached). These results demonstrate that effective cellulose-containing material processing into simple sugars is possible. Simple sugars derived from CCM using P. verruculosum preparation are a promising feedstock for the microbiological production of biofuels (bioethanol and biobutanol), aminoacids, and organic acids (e.g., lactic acid for polylactic acid production).