Various types of behavior due to plastic instability under uniaxial tension and compression are numerically investigated regarding sheet materials, plane strain blocks, and cylindrical bars and hollow cylinders. The code GOLDA for analysis of large elastic-plastic deformation previously developed by the author is used, which is one of quasi-static explicit FEM programs. Both of diffuse type and localized type of instability are concerned with. The role of vertex-hardening in plastic instability is payed attention, by using the J2G (J2-Gotoh`s corner theory) as the plasticity constitutive equation, which was proposed previously by the au­thor and is a kind of vertex-hardening theory. Following results are mainly derived. 1) In plane strain ten­sion, shear-type strain localization is realized by the use of J2G, but not by the conventional J2F (J2-flow theory). In axisymmetric tension of a cylindrical solid bar, however, such strain localization would never appear even by J2G, as expected by the experiment. 2) In axisymmetric tension of a hollow cylinder under the condition of no contractlion of its bore (therefore, in almost plane strain state with no circumferential strain), it is found that shear-type strain localization could occur. This is realized again by the use of J2G. whereas J2F never allows such strain localization. 3) In compression under the embedded edges condition. it is found that a sheet with initial aspect ratio of 2:1 (in height: breadth) yields double barreling, whereas a plane strain block yields double barreling at the initial aspect ratio of 3:1, not at 2:1 though expected from the conventional slip-line theory. As for a cylindrical solid bar, double barreling appears for the initial as­pect ratio of 2:1 but only for higher n-vaiue (the strain hardening exponent), say n=0.5. 4) As for barreling mode, when thick-walled axisymmetric tubes with the initial ratio of thickness to inner diameter 1/5 to 1/3 are compressed axially, corresponding to the initial aspect ratios of 3:1, 2:1 and 1:1, triple barreling, double barreling and single barreling appear, respectively. 5) It is found that thin-walled tubes buckle in a pro­gressive periodic mode with almost stationary compressive load under axial compression. Thus it can be used as a simplified model for buckling of more complex structures such as the honeycomb.