This study examined the dynamic relationships among the components of the Simple View of Reading (SVR) in a transparent orthography (Finnish) and the predictive value of cognitive skills (phonological awareness, letter knowledge, rapid naming, and vocabulary) on the SVR components. Altogether, 1,815 Finnish children were followed from kindergarten to Grade 3. Their cognitive skills were assessed in kindergarten, listening comprehension and reading fluency in Grades 1 and 2, and reading comprehension in Grades 1–3. Reading fluency and listening comprehension accounted for 37% of the variance in reading comprehension in Grade 2 and 28% in Grade 3. The direct effect of reading fluency on reading comprehension disappeared after Grade 1, whereas the effect of listening comprehension remained significant across time. Cognitive skills predicted reading comprehension mainly indirectly via listening comprehension and reading fluency in Grade 1. These findings support the validity of the SVR model in the context of a transparent orthography, but they also show that the direct effect of reading fluency on reading comprehension wanes after the early school years.