In this paper, the nonlinear creep behaviour of additive-manufactured carbon fibre-reinforced polyethylene terephthalate (CF-PET) is characterised using experimental, theoretical and computational methods. The experimental approach investigates the influence of infill orientations on the creep deformation of the material. For the study, samples at 0°, 45○, and 90° infill orientations are produced with 90% infill density using fused filament fabrication (FFF). The infill orientation parameter highly influences the creep behaviour. Increasing the infill orientation from 0° to 90° monotonically improves the creep resistance of the material, which can be explained by orientation of the fibre-matrix reinforcement towards the uniaxial stresses. Surface examinations of creep-ruptured samples via scanning electron microscopy (SEM) reveal that a combination of matrix failure, fibre pull-out, fibre-matrix debonding, inter-layer debonding, and the presence of voids cause the fractures. Based on the experimental data, the primary and secondary creep responses are modelled theoretically and computationally. The theoretical model is based on the dependence of the material's creep on stress and time parameters at the transient and steady state stages. Combined stress and time functions are used to model the creep of the material. Parallelly, two-dimensional (2D) finite element (FE) analyses are made on COMSOL Multiphysics to model the creep computationally. The approach is based on the superposition of Norton's and Garofalo's creep models with predefined time hardening property. The results of the modelling are in good agreement with the experimental findings, showing a maximum of 1.04 % for the theoretical, and 2.9 % for the computational approaches.