We analysed all the Holocene structures defining the Fremrinamar Fissure Swarm (FFS), in the Northern Volcanic Zone of Iceland, through the interpretation of aerial photos, orthomosaics and Digital Surface Models (DSMs), and field surveys. We measured the strike, dip, length and kinematics of 761 normal faults and reconstructed the slip profile of 76 main faults (length >2 km), with the purpose of evaluating the overall direction of along-axis rift propagation. We also measured the strike of 146 eruptive fissures and 1,128 extension fractures. A total of 421 faults dip towards the east and 340 dip towards the west, mainly striking N0°-10°E. Maximum fault length is 14.2 km, and W-dipping faults are longer than E-dipping faults. The majority of eruptive fissures strike N10°-20°E, and are concentrated in the southern part of the FFS, around the Fremrinamar central volcano. Extension fractures mainly strike N0°-10°E, with a maximum length of 2,508 m. We evaluated the variation of strike, fracture density and spacing along the FFS, and observed a change of its trend from NNE-SSW in the central-southern part, to NNW-SSE in the northern part. We interpret this evidence as the effect of the intersection with the Grimsey Lineament. The tapering of fault slip profiles indicates a main northward propagation of the rift, and thus of the deformation, interpreted as the effect of lateral propagation of dykes from the magma chamber below the central volcano towards the north. Such interpretation is also supported by the distribution of normal faults, vertical offset and dilation values, and also by the rift width, which tend to decrease towards the north.