We present Johnson CCD photometry in the B and V passbands for the stellar content of two intermediate age star clusters of the Large Magellanic Cloud (LMC), NGC 2134 and NGC 2249. In total 1613 stars are measured in NGC 2134 and 850 in NGC 2249. With the aid of two grids of stellar models calculated with convective overshoot (both from the core and the envelope) and different radiative opacities, we examine the color-magnitude diagrams (CMDs) and luminosity functions (LFs) of the clusters and estimate reddening, metallicity, and age. The opacities in usage are either the classical ones by Huebner et al. (1977) (therinafter LAOL) or those by Iglesias et al. (1992) (therinafter OPAL). Adopting the distance modulus of (m - M0) = 18.5 mag, we find that stellar models with metallicity Z = 0.008 are best suited to matech the main features of the observed CMDs. Accordingly, we get E(B-V) = 0.22 and the age of 1.9 x 108 yr for NGC 2134, and E(B-V) = 0.25 and the age of 5.5 x 108 yr for NGC 2249. Similar analysis is made using both the opacity source (OPAL or LAOL) bringing into evidence the major differences. Finally, for the sake of comparison we also examine the CMDs and LFs by means of models with identical opacities but the classical scheme of mixing. The LFs indicate that classical models with OPAL require unusually steep slopes of the initial mass function (IMF), x = 3.35 or greater, whereas models with overshoot and OPAL are consistent with the classical slope, x = 2.35.