In the preface of the dissertation is described the strategy of economy, ecology, security and protection of Croatian territory, founded on positive acts of the parliament of European democracy and on the fundaments of our historical experiences with an accent on the specific security of the borderline on the sea surface and in the underwater. Keeping in line, the models of determination of the parameters of hydroacoustical antenna in the underwater systems in this dissertation is presented as a fundamental factor of hydroacoustical scanning, prevention and protection of our interests on the sea. In the introduction of the explanation as long with the graphical presentation by the block scheme we have a general structure of hydroacoustical systems for the underwater observation and underwater weapons. In the first part of this dissertation the explained material comprises the important meaning of the parameters, their analyses and determination by the hydroacoustical measurements data. They are directly or indirectly used in the analysis of directivity index explained models of antenna in the second and the third part of the dissertation. In the first chapter of the second part of the dissertation two models of the piezoelectric transducers are presented. A simple cylindrical transducer and a model of the composite piezoelectric transducer described by the model of the ideal electrical transformation of electrical impedance and by matching of the phase of the electrical signal. Also, presented are mathematical forms of models of the ideal electrical transformer and the model of the ideal LC transformer with full control of the phase of electrical signals for the given piezoelectrical transducer. These hardware solutions of models for full control of the electrical parameters are especialiy coming in use on the composite hydroacoustical array which is presented in the second chapter. In the second chapter of the second part are presented and mathematicaliy performed the directivity pattern of the composite line array and the composite cylindrical array as the base for their electronical beam steering. Keeping in line, in the given mathematical expressions of the directivity pattern are used the parameters which are important in the analysis of the presented directivity index. The shown mathematical expressions are confirmed compared with a directivity pattern made during hydroacoustical measurements of a few foreign and one domestic array. Based on the simulation of beam steering graphical presentations it is possible to see and recognize a defect in array or foresee having false target. In the end of the second part of the dissertation are described standard models of the directivity index presentation as shown in the world literature. In the first item and the first chapter of the third part are described and compared the directivity indexes of hydroacoustical antennas of an ideal and. Keeping in line, in the second item of the first chapter is described a high influence of the suppressed minor lobe level and added major lobes on them. In the third chapter of the third part is described the antenna directivity index of the hydroacoustical active system with an ideal and idealized model of directivity pattern in the sea reverberation conditions.