We introduce knittable stitch meshes for modeling complex 3D knit structures that can be fabricated via knitting. We extend the concept of stitch mesh modeling, which provides a powerful 3D design interface for knit structures but lacks the ability to produce actually knittable models. Knittable stitch meshes ensure that the final model can be knitted. Moreover, they include novel representations for handling important shaping techniques that allow modeling more complex knit structures than prior methods. In particular, we introduce shift paths that connect the yarn for neighboring rows, general solutions for properly connecting pieces of knit fabric with mismatched knitting directions without introducing seams, and a new structure for representing short rows , a shaping technique for knitting that is crucial for creating various 3D forms, within the stitch mesh modeling framework. Our new 3D modeling interface allows for designing knittable structures with complex surface shapes and topologies, and our knittable stitch mesh structure contains all information needed for fabricating these shapes via knitting. Furthermore, we present a scheduling algorithm for providing step-by-step hand knitting instructions to a knitter, so that anyone who knows how to knit can reproduce the complex models that can be designed using our approach. We show a variety of 3D knit shapes and garment examples designed and knitted using our system.