  We analyze several problems related to off-shell structure of open string
sigma model by using a combination of derivative expansion and expansion in
powers of the fields. According to the sigma model approach to bosonic open
string theory, the tachyon effective action $S(T)$ coincides with the
renormalized partition function $Z(T)$ of sigma model on a disk, up to a term
vanishing on shell. On the other hand, $Z(T)$ is a generating functional of
perturbative open string scattering amplitudes. If $S(T) = Z(T)$, then there
should be no contribution of exchange diagrams to string amplitudes computed
using $S(T)$. We compute the cubic term in the effective action, and show that
it vanishes if some but not all external legs are on shell, and, therefore, any
exchange diagram involving the cubic term vanishes too. Then, we discuss a
problem of turning on nonrenormalizable boundary interactions, corresponding to
massive string modes. We compute the quadratic term for a symmetric tensor
field, and show that despite nonrenormalizability of the model one can
consistently remove all divergent terms, and obtain a quadratic action
reproducing the on-shell condition for the field. We also briefly discuss
fermionic (NS) sigma model, compute the tachyon quadratic term, and show that
it reproduces the correct tachyon mass. We note that turning on a massive
symmetric tensor field leads to the appearance of a term linear in it, which
can be removed by adding a higher-derivative term to the boundary of the disc.
