The expansion of intravascular stent may be considered as an extension in instable serial structure from the viewpoint of mechanics. Therandomization of the width and thickness of a stent will hare greatinfluence on the uniformity expansion in the instable serial structure. Inthis paper, a mathematical model to describe that problem is establishedon the basis of randomized unstable serial structure. The concept, methodand probability calculation formula of uniformity index are proposed.Regarding the serial structure made up of two expanded units, a detailedstudy is carried out on the influence of the random variation of beam thicknesson expansion uniformity indexes. We obtain the uniformity index probability'srelationships with beam thickness random variation, load variation andhardening coefficient variation. The research shows that materialharding coefficient has great effects on uniformity index when the totalexpansion displacement remains constant. The serial expansion theory ofrandom unstable structure provides an important guide to the design of new-typeintravascular stent.