A method is disclosed for 3D printing of soft polymeric material such as a hydrogel or elastomer for scaffolds or devices with embedded channels with tunable shape and size such as a channel inner diameter). The method utilizes extrusion based printing of polymer solutions usually referred as direct ink writing (DIW) or BioPlotting, and requires sequential printing of a photocurable polymer solution, herein, referred as the matrix material, and a sacrificial polymer solution that may dissolve in an aqueous media.