  Context. Scattering and absorption processes in stellar atmosphere affect the
center-to-limb variations of the intensity (CLVI) and the linear polarization
(CLVP) of stellar radiation. Aims. There are several theoretical and
observational studies of CLVI using different stellar models, however, most
studies of CLVP have concentrated on the solar atmosphere and have not
considered the CLVP in cooler non-gray stellar atmospheres at all. In this
paper, we present a theoretical study of the CLV of the intensity and the
linear polarization in continuum spectra of different spectral type stars.
Methods. We solve the radiative transfer equations for polarized light
iteratively assuming no magnetic field and considering a plane-parallel model
atmospheres and various opacities. Results. We calculate the CLVI and the CLVP
for Phoenix stellar model atmospheres for the range of effective temperatures
(4500K - 6900K), gravities (log g = 3.0 - 5.0), and wavelengths (4000 - 7000
{\AA}), which are tabulated and available at the Strasbourg astronomical Data
Center (CDS). In addition, we present several tests of our code and compare our
results with measurements and calculations of CLVI and the CLVP for the Sun.
The resulting CLVI are fitted with polynomials and their coefficients are
presented in this paper. Conclusions. For the stellar model atmospheres with
lower gravity and effective temperature the CLVP is larger.
