Typical antenna arrays are designed such that the active element pattern is symmetric around the broadside direction. However, applications exist, for example in satellite communication, where a symmetric pattern is not needed or even unwanted. This angular selectivity can be achieved using asymmetric elements. However, it is known that for well sampled infinite arrays the asymmetry of the active element pattern disappears. Although designs of under-sampled antenna arrays achieving an asymmetric active element pattern have been presented in literature, the fundamental properties of this type of arrays in terms of radiation characteristics have not been investigated in detail. This thesis studies the asymmetry in the active element pattern of a finite linear array of asymmetric elements. To this end an in-house method of moments code is developed in Matlab to simulate tilted dipoles in free space and in the proximity of a ground plane. The dependency of the asymmetry of the active element pattern on the inter-element distance, the skew angle of the elements and the number of elements in the array is analyzed and design rules are derived. Using entire domain basis functions, closed form expressions for spectral integrals and the periodicity of the array the implemented code enables the simulation of large arrays in a much shorter time compared to commercially available software, such as CST. Regarding the choice of antenna element, a dipole bent into a Z-shape is proposed as an alternative for a tilted dipole. This type of dipole can be defined to have an equivalent radiation pattern to that of a tilted dipole. This shape of dipole can be implemented using standard PCB technology using horizontal metal strips and vertical vias. The Z-shaped dipoles are analyzed using a method of moments code based on horizontal and vertical dipoles. The spectral Green's function of stratified media can be included in the spectral domain expressions to account for the presence of dielectric slabs in realistic designs.