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The aim of present paper is to investigate 3-dimensional ${\xi}$-projectively flt and $\tilde{\varphi}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is ${\xi}$-projectively flt then ${\Delta}{\beta}=0$. If additionally ${\beta}$ is constant then the manifold is ${\beta}$-para-Sasakian. Later, we proved that a 3-dimensional normal almost paracontact metric manifold is $\tilde{\varphi}$-projectively flt if and only if it is an Einstein manifold for ${\alpha},{\beta}=const$. Finally, we constructed an example to illustrate the results obtained in previous sections.
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