Creating multilayered channels for mimicking human blood vessels in thick tissues is the main challenge to overcome in organ biofabrication. Current three-dimensional (3D) printing strategies cannot effectively manufacture hollow channels with multiple layers. This study aims to propose a coaxial nozzle-assisted embedded 3D printing method in which core–shell filaments can be formed in a yield-stress matrix bath by extruding different ink materials through the corresponding channels. The materials selected for the core ink, shell ink, and matrix bath are Pluronic F127 (F127) and calcium chloride (CaCl2), sodium alginate (NaAlg), and poly(ethylene glycol) diacrylate (PEGDA) and nanoclay, respectively. After crosslinking the matrix bath and shell, the core layer made from the sacrificial ink (F127) is removed to generate a single-layered, hollow channel. In this work, the effects of ink material properties and operating conditions on core–shell filament formation have been systematically studied. The rheological and mechanical properties of the yield-stress matrix bath have been characterized as well. A thick tissue-like structure with embedded single-layered, hollow channels has been successfully printed for demonstration. Since it is feasible to design coaxial nozzles with a core–shell–shell architecture, the proposed method is technically extendable to create double-layered channels within a cellular tissue construct, accurately mimicking human blood vascular networks in thick tissues in the future.