The invention describes a system of industrial production of strained yogurt which enables the natural straining by means of separation means with the optimal use of the raw material with the least possible stressing of the raw material and with the minimum possible loss of useful ingredients in the whey which is removed after straining and with the optimal stability of the characteristics of the final product in each production batch. The invention describes the critical conditions of processes upstream of (namely before) the straining process such as the physiochemical features of the raw milk conditions of pasteurization and homogenization conditions of incubation etc and the stacks of suitably selected and positioned membranes that are used for the straining so that the final strained yogurt has the desired physiochemical features (proteins fat total solids) upon its exit from the straining rig. During the straining process the yogurt is consecutively strained at least twice and the process is complemented by the stages downstream of (namely after) the straining such as the conditions of cooling storage before packaging packaging conditions etc. which also are critical factors in order to realize the final outcome.