The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which innuclear mater makes the picture of a nucleon-nucleon interaction based on scalar (vector) meson exchange equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.