Technical Abstract: Genetic data collected from plant breeding and genetic studies may not be replicated in field designs even though field variation is present. In this study, we addressed this problem using spring wheat (Triticum eastivum L.) trial data collected from two locations. There were no intra-location replications and an extended additive-dominance model was used to account for field variation. We numerically evaluated the data from a simulation and estimated the variance components. As a demonstration, we analyzed three agronomic traits from the actual spring wheat data set. Results illustrated that these data could be effectively analyzed using an extended additive-dominance model, which was more comparable to a conventional model. Actual data analysis revealed that all traits were significantly influenced by systematic field variation. Additive effects were significant for all traits and dominance effects were significant for plant height and time-to-flowering. Genetic effects were predicted and used to demonstrate that most spring wheat lines developed by the South Dakota State University breeding program exhibited good general combining ability effects for yield improvement. Thus, this study provides a general framework to appropriately analyze data in situations where field crop data are collected from non-replicated designs.