The shear-parallel and shear-perpendicular linear mesoscale convective systems (MCSs) are studied by a three-dimensional nonhydrostatic cloud resolving model. On the basis of previous observational studies, a unique “reference layer” can be defined for both MCSs. A shear-parallel MCS can be distinguished from a shear-perpendicular MCS by the shear and moist instability in the reference layer only regardless of the shear at the other levels. This drastically simplifies the problem at hand. The reference layer is located below 400 mbar. It must be thicker than 200 mbar, and the mean shear of the layer must be larger than 2 m s−1 per 100 mbar. Its stratification is unstable or near neutral. The shear-parallel MCS is produced when the reference layer is near neutral or less unstable. In its first phase the new cells are produced by the basic wave propagation mechanism, modified by the shear. The growth rate is relatively small, and there is no cold pool in this phase. In the second phase the updrafts become strong and expand. A cold pool is formed along the shear-parallel direction, and the new cells are formed along the edge of the cold pool. The interaction between the shear and the updraft plays a major role in the formation of the shear-parallel MCSs. The cold pool outflow convergence and the interaction between the cold pool and the shear are also important in the second phase. On the other hand, the shear-perpendicular MCS is produced when the reference layer is highly unstable. The cold pool is always strong, and the interaction between the shear and cold pool plays a major role in the formation of the linear structure in agreement with the theory proposed by Rotunno et al. (1988). Sensitivity experiments indicate that both types of MCS organization can exist without precipitation or a cold pool and in the dry system. This finally provides a foundation for the theoretical analysis presented in the companion paper.