Additive manufacturing technologies make it possible to manufacture any product in layers based on a 3D computer model, but this issue is understudied. Therefore, this paper considers the problem of describing the effects of buckling arising in the three-dimensional printing of products containing elements whose length significantly exceeds their thickness or the characteristic size of the cross section. The behavior of these elements, from the point of view of material mechanics, can be described using models of plates or beams. In this study, we compare the results of calculations obtained using the model of non-stationary thermal conductivity and thermos-elasticity with experimental data for a specific element of printed product in which stability loss occurs. It was concluded that, at the initial moments of time, the lowest critical impact coefficient is realized, which in turn makes it the most dangerous phenomenon. The possibility of changing print parameters and product geometry to exclude the mentioned effects has been investigated. The considered structural element may lose stability during the building process. The results of solving the spectral problem indicated that over time the value of the critical effect decreases and asymptotically tends to a fixed minimum value.