Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering opensource, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in theC,C++and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.