Multi-stage, transversely fractured horizontal wellbores have the potential to greatly increase production from low permeability formations. Such completions are, however, susceptible to problems associated with near-wellbore tortuosity, particularly multiple fracturing from the same perforated interval. A criterion, based on that by Drucker and Prager, has been derived, which predicts the wellbore pressures required to initiate secondary multiple transverse hydraulic fractures in close proximity to primary fractures. Secondary fracture initiation pressures predicted by this new criterion compare reasonably well with those measured during a series of unique laboratory-scale multiple hydraulic fracture interaction tests. Both the multiple fracture initiation criterion and the laboratory results suggest that close proximity of primary hydraulic fractures increases the initiation pressures of secondary multiple fractures by the order of only 14%. This demonstrates that transversely fractured horizontal wellbores have limited capacities to resist the initiation of multiple fractures from adjacent perforations or intersecting heterogeneities. Petroleum engineers can use the multiple fracture initiation criterion when designing hydraulic fracture treatments to establish injection pressure limits, above which additional multiple fractures will initiate and propagate from the wellbore.