This study compared mothers and fathers' regulation with respect to 29 children with intellectual disability (ID) and 30 typically developing (TD) children, matched on their mental age (MA), as they solved eight tasks using physical materials and computers. Seven parents' regulatory strategies were coded as they supported their child's identification of the objective, planning, attention, motivation, joint attention, behaviour regulation and evaluation. Children's performance was scored. Regulation by the parents of the two groups did not differ significantly, regardless of the medium, except that the degree of parental regulation of the child's behaviour was greater in the ID group than in the TD group. In tasks involving the computer, we observed a higher degree of regulation of children's planning and a lower degree of regulation of their evaluation for the two groups. The parents displayed significantly less regulation with respect to the children with the highest MA than towards the children with the lowest MA, in each group. There was a significant interaction effect of medium and children's MA on overall parents' regulation and on their support of identification of objective and of planning. Most parental strategies were negatively linked with ID and TD children's performance in tasks. In both groups, with control for MA, parental support with the identification of the objective, with planning and with attention was negatively linked to the corresponding self-regulatory strategies of the children with each medium; however, parents' joint attention was positively linked with children's joint attention. (Contains 6 tables.)