Additive manufacturing is one of the most promising production technologies introduced in the last years. One extensive field of application of additive manufacturing is for prototyping, but 3D printed parts have also the potential to meet the requirements for functional components or production support. Fused filament fabrication (FFF) is the most popular additive manufacturing processes because of flexibility, reduced costs, and number of available materials concerning thermoplastics. Some of these materials have good thermal, electrical and mechanical properties, however they also exhibit a high dependence on process parameters and, in general, have lower properties than if the material is processed and manufactured by a classic process. In this paper monotonic, fatigue and creep behaviour of PLA under compression is studied, using cylindrical specimens tested according to ASTM D695, ISO 527, ASTM D7791 and ASTM D2990. A Design of Experiments was conducted to identify and quantify the effects of printing parameters on the compression behavior of these specimens. From best set of parameters, specimens were fabricated and tested under tension, fatigue (compression–compression) and creep (compression) to identify their performance and the failure mechanisms. It was observed that compressive strength is linearly dependent with the density of the samples, but for fatigue no such relation was found. The results obtained characterize the behaviour of PLA material produced by FFF under compression and can be useful for quality control and to support the design of parts that to work under compressive loads.