Bioprinting has many potential applications in drug screening, tissue engineering, and regenerative medicine. In extrusion-based bioprinting, the extruded strand is the fundamental building block for printed constructs and needs to be of good quality and continuous in structure. In recent years, many studies have been conducted on extrusion-based bioprinting. However, values of process parameters leading to continuous extrusion of strands have rarely been reported. In this paper, feasible regions of bioink composition, extrusion pressure, and needle size for continuous strand extrusion have been evaluated. The information on feasible regions for extruding continuous strands, provided in this paper, can be useful in deciding appropriate extrusion pressure and needle size for the bioink of different compositions (ratios of alginate:methylcellulose) in extrusion-based bioprinting.