The authors consider the motion of a compact body \(B\subset \mathbb{R}^3\) in an incompressible second grade fluid with the velocity field \(V\), pressure \(p\), and the exterior body force \(f\), where \(\lim_{| x|\to \infty}v(x) =v_\infty\). Put for brevity \(\Omega= R^3 \setminus \vec B\), \(\|\cdot \|_{m,q} =\| \cdot\|_{W^{m,q} (\Omega)}\), \(\|\cdot \|_q= \|\cdot \|_{L^q (\Omega)}\). The main result can be formulated as follows: let \(k \geq 1\) be an integer, \(\Omega\in C^{k+2}\), \(f\in W^{k,2} (\Omega) \cap L^{6/5} (\Omega)\), \(\| f\|_{k,2} +\| f\|_{6/5} \leq\text{const}\), \(0<| v_\infty |<\text{const}\). Then the above problem admits a unique solution \((v,p)\) such that \((v-v_\infty)\in L^4(\Omega)\), \(\nabla v\in W^{k+1,2} (\Omega)\), \(p\in W^{k,2} (\Omega)\) and \[ | v_\infty |^{1/4} \| v-v_\infty \|_4+ \|\nabla v\|_{k+1,2} +\| p\|_{k,2} \leq\text{const} \bigl(\| f\|_{k,2} +\| f\|_{6/5} +| v_\infty |\bigr). \] The proof is based on a decomposition procedure and on the investigation of two auxiliary subproblems: an Oseen system, and a transport equation.