A new modeling of elastic solids capable of polar description is presented. The primary d.o.f. of a material particle is the rototranslation as a whole. By resorting to the algebra of dual numbers, the rototranslation is represented by an orthonormal dual tensor that inherits all the properties of the rotation. A variational formulation fit for the proposed modeling is outlined and reduced to the case of non-polar materials. The discrete problem exploits consistent multiplicative interpolation and updating technique of the kinematical field. The first results of the finite-element implementation concern simulations of high geometrical nonlinearities in bending dominated problems.