Starting from the recent UNICEF publications on child poverty in the developed countries, which received a wide audience in the political and scientific world, in this paper we further analyze the UNICEF study data base and present three composite indices that are multidimensional and quantitatively measures of child well-being. While the original UNICEF studies simply added together the ranks on different measurement scales, we present a much more sophisticated approach, with the first of our indicators being a non-parametric measure while the remaining two are parametric. In the non-parametric index of child welfare, the well-being indicators are given same weights in their aggregation to form different components from which an overall index is being constructed. Two different forms of the parametric index are estimated by using principal component analysis. The first model uses a pool of all indicators without classification of the indicators by type of well-being, while the second model estimates first the sub-components separately and then uses the share of variance explained by each principal component to compute the weighted average of each component and their aggregation into an index of overall child well-being. The indices indicate which countries have the best system of child welfare and show how child well-being varies across countries and regions. The indices are composed of six well-being components: material, health and safety, educational well-being, family and peer relationships, behaviours and risks and subjective well-being. Each of the components is generated from a number of well-being sub-indicators.