Using the methods of effective moduli and finite elements, the effective properties of nanoporous thermoelastic transversely isotropic materials were studied for simple random and for closed structures of porosity. Nanoscale effects were modelled in the framework of the Gurtin-Murdoch model of interface stresses and of the high conductivity model. The modelling and solution of homogenization problems was performed in the ANSYS package, while structures of representative volumes with closed porosity were created in the ACELAN-COMPOS package. The effect of porosity, types of representative volumes and pore sizes on the values of the effective modules of nanoporous titanium is analysed. © 2020, Springer Nature Switzerland AG.