The aim of the present paper is to study the entropic elasticity of the dsDNA molecule, having a crystallographic length L of the order of 10–30 persistence lengths A, when it is subject to spatial obstructions. We have not tried to obtain the single-molecule partition function by solving a Schödringer-like equation. We prefer to restrict our considerations to a discretized version of the worm-like chain model with an added one-monomer potential, simulating the spatial constraints. We derived the transfer matrix connecting the partition functions relative to adjacent 'effective monomers' directly from the discretized Boltzmann formula. We have plugged Dirac δ-functions in the functional integral that are adequate to ensure that the monomer coordinate and the tangent vector are independent variables. The partition function is, then, given by an iterative process which is both numerically efficient and physically transparent. As a test of our discretized approach, we have studied two configurations involving a dsDNA molecule confined between a pair of parallel plates. One molecule end is anchored to one plate by a biochemical bond. A stretching force F, normal to the plates, is pulling the other end away. In the first case, the crystallographic length L is smaller than the two-plate distance L₀. The molecule feels, then, only the anchoring barrier effect. The predicted elongation versus force curve is pushed upward with respect to the WLC (worm-like chain) model result. This effect is most spectacular in the low force regime. For large forces, say, F_high = 5 k_B T/A, the elongation versus L is very well fitted by a straight line with a slope given by the standard WLC model and a constant term . In the second case, L takes values up to L_max = 1.5 L₀. With a stretching force still equal to F_high, the standard WLC model predicts that the molecule cannot fit within the plates when L > L_* = 1.29L₀. We have studied the evolution of the elongation derivative with respect to L, together with the mean square free-end fluctuations along the force. They both exhibit a sharp decrease when L ≥ L₀. We present a semiquantitative argument suggesting that the terminal segment involving 20% of the internal monomers flattens against the repulsive barrier when . In conclusion, we suggest extensions of the present work, relevant to the analysis of micromanipulation experiments. Finally, we have gathered in an appendix formal developments, leading to a precise relation between the transfer matrix and the Hamiltonian methods for the study of spatially constrained dsDNA.