Bolted joints are often the choice for mechanical fastening in aircraft structures due to the ease of assembly and disassembly and inspection. However, bolted joints in composite structures introduce additional design challenges. The orthotropy of the laminates can lead to higher stress concentrations around the holes and can become a source of damage in the composite parts. The failure analysis of these joints in bearing loads is crucial as these aircraft reach the end of their initially designed lifetime and the potential for extended use is evaluated. The ASTM D5961 Procedure-A test fixture is used to test bearing strength of composites that replicate bolted joints with protruding heads. Countersunk bolted joints are widely preferred to straight hole joints in the aerospace industry due to their aerodynamic advantages. The bearing test procedure standard recommends the use of single lap joints for bearing tests on countersunk fasteners heads. ASTM D5961 Procedure-C is the suggested option to obtain bearing strength of countersunk composite bolted joints. Previous experimental investigations of composite bolted joints with countersunk fasteners have shown that the bolt and specimen bending and clearances of the bolt and bolt hole lead to changes in out-of-plane pressure. Furthermore, clamp-up loading contributes to uncertainty in the obtained bearing strength values. Procedure-C test results are also strongly dependent on the applied bolt torque or bolt preload. For thick composites where bending effects are negligible, using the standard ASTM D5961 Procedure-C single lap joint does not appears to represent reality. This paper investigates use of a modified fixture derived from the ASTM D5961 Procedure-C to accommodate a countersunk fastener in a double lap shear test. Numerical finite element analysis simulations of bolted composite joint tests with straight and countersunk holes using the original and modified fixtures are performed using ABAQUS software. The resulting deformations of the specimen and the pins, the in-plane and out of plane stress distributions at the bearing location are compared. The tests of bearing strength of composites with countersunk holes show significant dependency on the relative stiffness of the specimen, fastener and fixture. The choice of test methods can also lead to significant variances in results. The Modified Procedure-A is can be adopted as valid procedure for bearing tests of composite bolted joints with countersunk fasteners. However, it does not yield valid results in testing composites using fixed standard physical dimensions for fixtures and test specimens. The test specimens and fixtures should be scaled according to their stiffness to reflect the structural joint configuration.