Material extrusion additive manufacturing (ME-AM) techniques have been recently introduced for core–shell polymer manufacturing. Using ME-AM for core–shell manufacturing offers improved mechanical properties and dimensional accuracy over conventional 3D-printed polymer. Operating parameters play an important role in forming the overall quality of the 3D-printed manufactured products. Here we use numerical simulations within the framework of computation fluid dynamics (CFD) to identify the best combination of operating parameters for the 3D printing of a core–shell polymer strand. The objectives of these CFD simulations are to find strands with an ultimate volume fraction of core polymer. At the same time, complete encapsulations are obtained for the core polymer inside the shell one. In this model, the deposition flow is controlled by three dimensionless parameters: (i) the diameter ratio of core material to the nozzle, $d/D$; (ii) the normalised gap between the extruder and the build plate, $t/D$; (iii) the velocity ratio of the moving build plate to the average velocity inside the nozzle, $V/U$. Numerical results of the deposited strands’ cross-sections demonstrate the effects of controlling parameters on the encapsulation of the core material inside the shell and the shape and size of the strand. Overall we find that the best operating parameters are a diameter ratio of $d/D=0.7$, a normalised gap of $t/D=1$, and a velocity ratio of $V/U=1$.