Skin is our primary barrier to the outside world, protecting us from physical, biological and chemical threats. Developing innovative products that preserve and improve skin barrier function requires a thorough understanding of the mechanisms underlying barrier response to topical applications. In many fields, computer simulations already facilitate understanding, thus accelerating innovation. Simulations of software models allow scientists to test hypothesized mechanisms by comparing predicted results to physical observations. They also enable virtual product optimization, without physical experiments, once mechanisms have been validated. The physical accessibility and abundant knowledge of skin structure makes it a prime candidate for computational modeling. In this article, we describe a computational multiscale multicellular skin model used to simulate growth and response of the epidermal barrier. The model integrates several modeling styles and mathematical frameworks including ordinary differential equations, partial differential equations, discrete agent-based modeling and discrete element methods. Specifically, to capture cell biology and physical transport, we combined four distinct sub-models from existing literature. We also implemented methods for elastic biomechanics. Our software implementation of the model is compatible with the high-performance computing simulation platform Biocellion. The integrated model recapitulates barrier formation, homeostasis and response to environmental, chemical and mechanical perturbation. This work exemplifies methodology for integrating models of vastly different styles. The methodology enables us to effectively build on existing knowledge and produce "whole-system" tissue models capable of displaying emergent properties. It also illustrates the inherent technical difficulties associated with the mounting complexity of describing biological systems at high fidelity. Among the challenges are validation of the science, the mathematical representations approximating the science and the software implementing these representations. Responsibility for a discrepancy observed between in silico and in vitro results may as easily lie at one of these three levels as at another, demanding that any sustainable modeling endeavor engage expertise from biology, mathematics and computing.