The aim of the research presented in the paper was to determine the co-occurrence of the personality metatraits of the Stability and Plasticity of parents described in the Circumplex Personality Model CPM of Włodzimierz Strus, Jan Cieciuch and Tomasz Rowiński with the parental goals they set for pre-school age children. The study sought to answer the following questions: What parental goals are most ofte chosen by parents of pre-school children, depending on the level of parents’ Alfa-plus (Stability) personality metatrait? What parental goals are most often chosen by parents of pre-school children, depending on the level of metatraits of the Beta-plus personality (Plasticity)? The research sample was 128 adults, parents of preschool children (3-6 years). Thee research was conducted via the Internet, using the University System of On-line Research, operating at the Cardinal Stefan Wyszyński University in Warsaw. The algorithms used for the analysis were: a) text-mining, b) cluster analysis and c) decision trees. The relationship between the parents’ personality traits of the Alfa -plus (Stability) and Beta-plus (Plasticity) was revealed, and the positive and negative parental goals they choose. The main result of the study was that parents promote the development in children personality traits similar to theirs, and counteract the development of opposite personality traits. The effect was observed in both groups of parents (having the highest results in the Alfa-plus traits, and having the highest scores in terms of Beta-plus traits).