This paper regards the minimum weight problem of spatial systems, known in the literature as Rozvany–Prager archgrids. Their architectural role is to transmit a load of fixed intensity to the line of supports located at the boundary of a given plane domain. The system consists of arches spaced apart from one another, hence the mechanics of such a system is that of a gridwork shell and not a shell continuum. Mathematically, description of an archgrid falls into the class of Michell frames. Therefore, in our approach, we make use of the plastic design paradigm – it states that optimal bar structure is at the verge of plastic failure, with bars uniformly stressed to the limit value in compression, or tension. In the case of archgrid optimization, only compression is allowed and this limitation introduces an additional design constraint. The main goal of this paper is computational, thus the general variational framework of the optimization problem is reformulated in the discrete setting, involving the methods of linear algebra. Numerics of the discrete approach to Rozvany–Prager archgrids is considered from the novel perspective based on second-order cone programming (SOCP). Procedures used for solving the examples are coded in MATLAB combined with MOSEK optimization toolbox for SOCP routines.