Response Surface Methodology is a collection of mathematical and statistical techniques useful for analyzing problems where several independent variables influence a dependent variable or response and the goal is to find the product mix to optimize this response. As the estimation of slope of response surface occurs frequently in practical situations,. The authors have introduced the concept of embedding and constructed v dimensional second order slope rotatable design from a known (v-1) dimensional second order slope rotatable design using embedding techniques. Group-Divisibility in Second Order Slope Rotatable Designs (SOSRD) is also introduced and constructed various designs in view of its practical applicability. As all existing second order slope rotatable designs are five level designs, the authors constructed second order slope rotatable designs with factors each at four levels using balanced incomplete block designs and central composite type design points. They also introduced and constructed the Third Order Slope Rotatable Designs (TOSRD) over an axial direction using Central Composite Designs and Doubly Balanced Incomplete Block Designs

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