This article investigates the behavior of cultural influence networks over time, using a computer simulation based on a formal model of cultural transmission in organizations. In the formal model, every organizational member exerts some cultural influence on, and is influenced by, every other member; these influence paths constitute a dense social network and the weights of paths (ties) vary throughout the network. Over time, each organizational member’s enculturation level changes in response to influence from other members, and the influence weight of each path changes in relationship to the cultural similarity of the individuals connected by the path. Virtual experiments explore the configuration and evolution of the cultural influence network under varying demographic conditions and influence principles. Demographic effects are studied by varying organizational size, hiring selectivity and turnover rates. Two principles for determining initial influence path weights are examined, cohort-based influence and random influence. The simulations show that the cultural influence network evolves over time to a robust configuration, fluctuating around a stable dynamic equilibrium as individuals enter and leave the organization. As turnover rates rise, cohort-based influence strengthens the influence network and reduces network inequality. In this model, cohort-based influence processes promote cultural stability in organizations.