Dry masonry is a type of construction that is nowadays used to a limited extent in the construction sector, including the housing sector. A lack of codified computational methods enabling engineers to design consciously is one of the factors limiting the development of dry walls. This article presents results from testing an innovative solution for dry masonry made of medium-size elements with expanded perlite aggregate. Material with this type of aggregate has a low bulk density (390 ± 10% kg/m3), which allows the production of large blocks and significantly reduces the value of the thermal conductivity coefficient λ = 0.084 ± 0.003 W/m·K. The results obtained were used to determine material parameters for designing a structure mainly exposed to vertical load. The important practical significance of the presented research results from the lack of provisions, specifications or standards allowing for the design, calculation and construction of dry masonry; it is not possible to analyse the behaviour of this type of structure and to design it consciously and safely. The presented research is therefore an important source of information on mechanical parameters essential for the design of structures and provides tools for this. As a result of the tests of nine panels, the mean compressive strength was determined (1.085 N/mm2), and then the procedure of “design assisted by testing” implemented into Eurocode was used to determine characteristic (0.873 N/mm2) and design compressive strength (0.565 N/mm2). Using the relationships σ-ε, an attempt was made to identify material models for the linear and non-linear analysis of the structure and for designing cross-sections. The material models were made considering increased non-linear deformations of a structure under low stresses (the compression toe) which are true and typical for dry masonry. A specific deformability of dry masonry, slightly different to that in masonry structures joined together with mortar, also affects the reduction factor for load-bearing capacity due to second-order effects. Reduction factors determined from true non-linear deformations were lower than the values specified by EC6 for masonry structures.