The article shows the effectiveness of the use of polymer additives for the production of fine-grained concrete mixtures and concretes based on using coal fly ash, which can be used as working mixtures for a 3D printer. Using mathematical planning of experiments, a set of experimental–statistical models was obtained that describes the influence of mixture composition factors including copolymer additive on the most important properties of ash-containing concrete mixtures and concretes for 3D concrete printing in the presence of a hardening accelerator additive. It is shown that when the dry mixture is mixed in water, the redispersed polymer powders are converted into an adhesive polymer dispersion, which, when the solution cures, creates “rubber bridges” in its pores and at the border with the base. They have high tensile strength and elastically reinforce the cement stone; in addition, they are also capable of not only significantly increasing the adhesion between the layers of the extruded mixture, but also significantly smoothing out such shortcomings of the cement stone as increased brittleness, low ultimate elongation, and a tendency to cracking.