Abstract: Local permanent damage caused by monotonic or cyclic load may lead to failure for structural components in aerospace, petrochemical, nuclear power and other engineering fields, and the mechanical properties of materials under monotonic and cyclic load conditions are the basis of service safety evaluation and anti-fatigue design for structures. Due to the limitation of material size and sampling for service structure material, it is vital to investigate the testing method to obtain the mechanical properties of materials under monotonic and cyclic load conditions by millimeter-sized and centimeter-sized specimen. In this paper, based on the energy density equivalence and dimensional analysis, metal sheet hourglass specimens with isotropic material and stress-strain relationship conform to Ramberg-Osgood law. Material constitutive relation parameters are described, small thin specimen geometry size of elastic-plastic displacement load relations theory equation and the energy density of representative volume unit value point of the theoretical equation of equivalent stress, equivalent strain were put forward, and then the sheet metal hourglass specimens cycle under steady or monotonous mode of relationship between equivalent stress and strain test method were put forward. The main work is as follows. A theoretical equation for the elastic-plastic displacement-load relationship of a sheet hourglass specimen was proposed, and the theoretical equations for the equivalent stress and strain of the representative volume element (RVE) at the median energy density point were derived. Verifications for results were completed using 40 materials with imaginary finite element analysis (FEA) constitutive relationship and 6 geometrical size of sheet hourglass specimens, and the results show that the semi-analytical equations and analytic equation have generally applicable and good accuracy. The monotonic tensile stress-strain relationship or the stress-strain relationship under steady-state symmetric cycle could be obtained directly from the equivalent stress-strain relationship test method of the sheet metal hourglass specimen under cyclic steady state or monotonic state. In order to verify the effectiveness of the proposed method, the results of tensile and variable amplitude symmetric strain cyclic tests of standard round bar specimens were compared. The monotonic tensile tests for two materials and one geometry and symmetric strain cyclic tests with various strain amplitude for five materials and one geometry were completed for standard round bar specimens and sheet hourglass specimens respectively. And the results show that monotonic and cyclic stress-strain relationships of materials predicted by the analytical model with sheet funnel specimens agree well with those tested by standard method with round bar specimens.