3D printing by fused filament fabrication (FFF) provides an innovative manufacturing method for complex geometry components. Since FFF is a layered manufacturing process, effects of process parameters are of concern when plastic materials such as polylactic acid (PLA), polystyrene and nylon are used. This study explores how the process parameters, e.g. build orientation and infill pattern/density, affect the mechanical response of PLA samples produced using FFF. Digital image correlation (DIC) was employed to get full-field surface-strain measurements. The results show the influence of build orientation and infill density is significant. For on-edge orientation, the tensile strength and Young’s modulus were 55 MPa and 3.5 GPa respectively, which were about 91% and 40% less for the upright orientation, demonstrating a significant anisotropy. The tensile strength and Young’s modulus increased with increasing infill density. In contrast, different infill patterns have no significant effect. Considering the influence of build orientation, based on the experimental results, a constitutive model derived from the laminate plate theory was employed. The material parameters were determined by tensile tests. Results demonstrated a reasonable agreement between the experimental data and the predictive model. Similar anisotropy to tension was observed in shear tests; shear modulus and shear strength for 45° flat orientation were about 1.55 GPa and 36 MPa, whereas for upright specimens they were about 0.95 GPa and 18 MPa, respectively. The findings provide a framework for systematic mechanical characterisation of 3D-printed polymers and potential ways of choosing process parameters to maximise performance for a given design.