Studies have demonstrated significant associations between executive function (EF) and reading ability. Many of these studies have evaluated this association through composite EF skills. In this study, we evaluated the indirect effects of working memory (WM) and cognitive flexibility (CF) in the relation between kindergarten socioeconomic status (SES) and first-grade reading achievement. Through a two-period estimation of mediating effects, we also examined these same relationships within low-achieving (LA) and typically developing (TD) readers. For these investigations, nationally representative data from the United States were utilised from the Early Childhood Longitudinal Study, Kindergarten Class of 2010-2011. Results revealed significant EF and SES differences between TD and LA readers. Additionally, WM mediated around 11% of the association between kindergarten SES and first-grade reading achievement while CF mediated 2.6%. The comparison of results between LA and TD readers yielded differences in mediating effects. For LA readers, 15% of the association was mediated by WM, but for TD only, 7.8% was mediated. CF mediated a small amount in both groups. Both WM and CF mediate the relation between kindergarten SES and first-grade reading achievement. These findings are important because they provide clear evidence that EF ability may partially account for achievement gaps in reading ability from kindergarten to first grade.