This　paper　discusses　the　fundamental　assumptions,　the　differential　equations,　and　the　variational　principles　of　discontinuous　form　belonging　to　a　new　developing　branch　of　science-the　solid　mechanics　of　discrete　form.　The　solid　mechanics　of　discrete　form　belongs　to　the　branch　of　science　of　discrete　medium　mechanics　which　is　the　developing　direction　of　the　mechanics　for　the　present.　Based　on　the　solid　system　with　discretization　and　separability,　the　unknown　functions　with　discontinuity　in　defined　regions　and　the　defined　regions　with　variable　boundaries,　the　mechanics　systems　to　solve　the　solid　displacements,　strains　and　stresses　in　various　cases　are　called　the　solid　mechanics　of　discrete　form.　When　the　unknown　functions　are　sufficiently　smooth　functions　in　the　whole　defined　region　and　the　effects　of　the　variable　boundaries　are　disregarded,　the　solid　mechanics　of　discrete　form　will　degenerate　into　the　classical　solid　mechanics　belonging　to　continuum　mechanics:　Its　variational　principles　will　degenerate　into　the　classical　variational　principles　with　the　same　cases.　©　1983　Hust　Press.