Single‐input single‐output (SISO) three‐dimensional (3D) wideband indoor directional measurements collected in a factory environment and an office environment at 38 and 70 GHz are presented. 3D single‐input multiple‐output (SIMO) dual polarised measurements with 1 × 2 antenna configurations were also carried out in a meeting room, a conference room, and an office room at the 60 GHz band. The measurements cover both azimuth and elevation by rotating the directional antenna (RDA) at the receiver side. Different statistical channel parameters such as power delay profile, power angle profile, root‐mean‐square delay spread, angular spread, and path loss were estimated for different possible antenna orientations between the transmitter and the receiver, which include line‐of‐sight, obstructed line‐of‐sight, and non‐line‐of‐sight. The polarisation effects on path loss models and the delay and angular spread models based on the surface area of the environment are studied. The results will be valuable for the design of indoor millimetre wave cellular networks.