FIELD: mining industry. SUBSTANCE: described are aqueous drilling muds comprising special classes of polymers which act as inhibitors of crushing and swelling of shales in treating petroleum or gas collectors. Aqueous drilling or collecting mud comprise polymers with properties of inhibition for shales. These polymers are dissolved in mud and are formed from 50-100 mole % of monomers of formula: 
wherein R1 is selected from H and C1-C4 alkyl groups; R2 is selected from C1-C4 alkyl groups, -C(CH3)2CH2COCH3, -CH=CH2 and -C(CH3)=CH2; R3 is selected from H, C1-C4 alkyl groups, CH2=CH- and CH2=C(CH3)-; when R3 is H or C1-C4 alkyl, then R1 is H, and R2 is -CH=CH2 or -C(CH3)=CH2, and when R2 is C(CH3)2CH2COCH3, then R1 is H, and other nonionic ethylenically unsaturated monomers 0-50 mole %, polymer is formed without changing formed of any monomer units and has molecular weight of 700,000 or less. Method of drilling shaft of borehole in shale-containing rock envisages removing from borehole and washing away material onto surface of borehole shaft with aqueous drilling mud as indicated above and also identifying the fat that drilling is carried out through shale-containing rock. EFFECT: reducing crushing shales to minimum. 13 cl, 7 ex, 6 tbl
