The scaffold has demountable elements which can be connected to one another to make up lateral frames that incorporate vertical members, flooring platforms or planks, diagonal bracing bars, and handrail poles, and is characterized in that the said lateral frames are composed of an inverted L-shaped element and a straight pole which is connected, by a quick coupling without clearance, to the horizontal arm of the L, and is optionally complemented by further poles to make up the lateral frames, both the straight pole and the vertical or longer arm of the inverted L-shaped element being provided with quick couplings with swinging clamping pieces which are intended to receive the flattened ends of reinforcing tie rods and safety-rail poles.