Aim of the study: According to David H. Olson’s circumplex model of family systems, there are particular dimensions that form the basis for good adaptation and growth, namely flexibility, cohesion, communication and family life satisfaction. The study explores the connections between these dimensions of family functioning, socioeconomic status of the family and educational achievements (reading, writing and numeracy skills) of preschool and early school-age children. Method: The subjects were 105 children, aged 5–6, and 105 parents of these children from the Silesian region in Poland. The parents filled out Family Rating Scales – Skale Oceny Rodziny, SOR (Margasiński, 2009), i.e. the Polish adaptation of the Family Adaptability and Cohesion Evaluation Scale known as FACES IV (Olson and Gorall, 2006), and demographic questions to assess the family’s socioeconomic status (SES). The children completed a computer-adaptive test of school ability at the start of school (Test Umiejętności na Starcie Szkolnym, TUNSS, Kaczan and Rycielski, 2014). Results: Multivariate structural equation modeling (SEM) was performed, confirming both SES and SOR to influence the children’s level of school skills at the start of school. The children’s age (expressed in months) presented as an important variable in the model. These factors explain 78% of variance of early school abilities. The number of books and mother’s education level were found to be the variables the most closely linked to school abilities amongst the SES factors. Children with a balanced family system background reached better scores in school abilities than children from unbalanced family systems.