This article explores the viscoelastic properties of polyethylene terephthalate glycol samples created by fused filament fabrication, emphasising the anisotropy introduced during fabrication. The samples were fabricated with filament direction within samples aligned along the principal axis or perpendicular. A group of samples was loaded with constant stress for 5 h, and a recovery phase with no applied stress was observed. Another group of samples was loaded for 20 h without an additional deformation recovery phase. The continuous constant stress application results on the sample were analysed, and an overall effect of anisotropy on the samples was observed. Several models describing viscoelastic deformation were considered to adhere to experimental data, with the Prony series and general cubic theory models used in the final analysis. The models could describe experimental results up to 50% and 70% of sample strength, respectively. The analysis confirmed the nonlinear behaviour of printed samples under constant stress and the significant effect of anisotropy introduced by the 3D printing process on the material’s elastic properties. The viscoelastic properties in both directions were described using the same parameters.