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We present in this paper spectral and spatial characteristics of terahertz emission from standard dipole antenna structures used as emitters depending on the substrate material. All antenna structures were lithographically fabricated on low-temperature (LT) grown, few-micrometers-thick gallium arsenide (GaAs) layers. To investigate the effect of the substrate material on the radiation pattern of terahertz beams, either semi-insulating gallium arsenide or high-resistivity silicon substrate wafers have been used. As detector a standard 40 µm long dipole antenna on a semi-insulating GaAs substrate with a low-temperature grown gallium arsenide layer on it has been employed; this configuration allows for broadband detection and is still efficient enough for the characterization purpose. Strong dependence of the radiation pattern on the substrate used for the terahertz source is demonstrated. The measured patterns and differences between the two cases of substrates are well explained by means of classical diffraction.