The article solves the problem of substantiating the production of birch plywood for construction purposes using phenol–formaldehyde binder at a reduced pressing temperature and reduced consumption of phenol–formaldehyde binder (PFB). When the pressing temperature drops to 100…105 °C, the phenol–formaldehyde binder does not reach its maximum degree of curing. With a decrease in binder consumption to 95…98 g per square meter of veneer surface and a decrease in pressing temperature to 105 °C, it is necessary to ensure the required mechanical properties—the strength of plywood during static bending and chipping along the adhesive layer, as well as a low thickness swelling after 24 h in water. To ensure the required level of physico-mechanical properties of plywood, modifiers were used in the work—copper acetate, resorcinol and copper resorcinate. The proportion of the modifier additive was 1.0…2.0% by weight of the phenol–formaldehyde binder. Using two-factor analysis of variance, the significance of the effect of the type of modifier and the proportion of the additive in the binder on plywood performance was mathematically verified. A regression mathematical model of the dependence of plywood thickness swelling on technological factors of the production process has been developed. Plywood based on a modified phenol–formaldehyde binder, manufactured with reduced binder consumption and reduced pressing temperature, has high strength and low thickness swelling. The results obtained can be recommended for use in the production of plywood for construction purposes.