We present three-dimensional ultrashort echo time Cones (3D-UTE-Cones) imaging as well as quantification of T2* and magnetization transfer ratio (MTR) of Achilles tendon and its enthesis of healthy volunteers and patients with psoriatic arthritis (PsA) using a 3T scanner. Quantitative T2*, T2 and magnetization transfer ratio (MTR) measurements of Achilles tendon and its enthesis were performed on healthy volunteers (n=7) and PsA patients (n=9) with 3D-UTE-Cones and clinical sequences at 3T. T2* was measured via single-component fitting of UTE images from two interleaved dual echo 3D-UTE-Cones acquisitions. MTR was measured with a dual echo 3D-UTE-Cones-MT sequence. Clinical morphological imaging and quantification of T2 with a Carr-Purcell-Meiboom-Gill (CPMG) sequence and MTR with a gradient recalled echo (GRE) sequence were also performed on each subject. T2* and MTR were analyzed for the two groups and the significance was evaluated. The 3D-UTE-Cones sequence provided high resolution imaging of entheses and tendons. Cones-T2* and Cones-MTR values were significantly higher for the PsA patients. GRE-MTR values showed no significant differences between the groups. No reliable T2 measurement could be achieved with the CPMG sequence due to insufficient signal from entheses and tendons. The 3D-UTE-Cones sequences can be used for morphological and quantitative evaluation of entheses and tendons in PsA patients.