In phononic quasi one-dimensional structures, there is a phenomenon of a phononic bandgap (PhBG), which means that waves of a given frequency do not propagate in the structure. The location and size of PhBG depend on the thickness of the layers, the type of materials used and their distribution in space. The theoretical study examined the transmission properties of quasi one-dimensional structures designed using a genetic algorithm (GA). The objective function minimized the transmission integral and integral of the absolute value of the transmission functions derivative (to eliminate high transmission peaks with a small half width) in a given frequency range. The paper shows the minimization of transmission in various frequency bands for a 40-layer structure. The distribution of multilayer structure transmission was obtained through the Transfer Matrix Method (TMM) algorithm. Structures surrounded by water were analyzed and built of layers of glass and epoxy resin.