Bricklaying has been one of the determinant technologies of the construction industry for several thousand years. Even in our modern times, it is one of the most commonly used fields of building construction technologies. There are several reasons, like the lack of human resources on the construction markets or the increasing demands on both reasonably short construction time and high construction quality, the combination of which leads to consideration of applying innovative, automated technologies in more and more fields. With the spread of these advanced techniques, changes and further development on the construction site can be predicted. One of these developing fields will be presumably the field of small, solid construction units, the innovation of which would result in changes regarding the elements and the technology too. In our research, automated bricklaying construction situations are modeled by applying a robotic arm equipped with a linear rail. Some new features are analyzed at the work of using automated systems. Namely, different brick wall construction methods are tested, measured, and analyzed to find optimal solutions for the cases of various sets of influencing factors, like element placement or palette arrangement.