Recently, the International Commission on Radiological Protection (ICRP) developed new mesh-type reference computational phantoms (MRCPs) that provide high deformability compared with the current voxel-type reference computational phantoms of ICRP Publication 110. Taking advantage of this deformability, in the present study, the MRCPs were deformed to five non-standing postures (i.e. walking, sitting, bending, kneeling, and squatting) by developing and using a systematic posture-change method based on the as-rigid-as-possible (ARAP) shape-deformation algorithm and motion-capture technology. The non-standing MRCPs were then implemented in the Geant4 Monte Carlo code to calculate a comprehensive dataset of dose coefficients (DCs) for photon external exposures. These include the dose coefficients for 29 individual organs/tissues and the dose coefficients for effective doses from 0.01 MeV to 10 GeV in the antero-posterior (AP), postero-anterior (PA), left-lateral (LLAT), right-lateral (RLAT), rotational (ROT), and isotropic (ISO) geometries. To investigate the dosimetric impact of posture, the DCs of the non-standing MRCPs were compared with those of the original MRCPs (in the standing posture). The results showed that organ/tissue doses are significantly influenced by posture, with arm position mostly influencing dose to organs/tissues in the torso region and leg position influencing dose in the pelvic region. For most cases, the gonads showed notably large differences, ranging from a few tens of percentage points to several orders of magnitude, depending on posture and irradiation geometry. The effective doses showed much smaller differences than the organ/tissue doses, but they were nonetheless significant: for example, the kneeling MRCPs in the AP geometry showed lower values at energies <10 MeV by up to 30% and greater values at higher energies by up to 40%. The presented results indicate that not only different irradiation geometries, but also different postures might be necessary in DC calculations for reliable dose estimates for radiological protection purposes.