This study evaluates the therapeutic tolerability of the use of Cognitive Processing Therapy (CPT) with propranolol in participants with Posttraumatic Stress Disorder (PTSD) and Alcohol Use Disorder (AUD). The investigators are planning to perform an initial proof -of- concept randomized, placebo- controlled trial evaluating propranolol in participants with PTSD and AUD starting CPT for 12 weeks with three post-treatment follow ups at week-16, week-20, and week-24.

Participants with current diagnosis of PTSD and AUD seeking treatment will be randomized to either a propranolol group (n=24) or placebo group (n=24) after enrollment. All participants will receive CPT for 12 weeks after randomization. Primary outcomes will be measured in both groups at the end of the study (week 12).

Inclusion Criteria:

1. Adults between 18 and 70 years old inclusively
2. Diagnosed with AUD in the past year (according to the Structured Clinical Interview for DSM-5 (SCID)25). This will include active drinkers and recently abstained drinkers.
3. has a minimum of two episodes of heavy drinking (≥5 drinks in a single day for men and ≥4 drinks in a single day for women) in the past 30 days as used in other trials26
4. Diagnosed with current (past 30 days) PTSD with the Clinician- Administered PTSD Scale for DSM-5 (CAPS-5) on screening27
5. On an antidepressant as treatment of PTSD (to ensure safety and homogeneity as PTSD treatment of study population). Antidepressants are the first-line treatment for PTSD as well major depression which commonly comorbid PTSD. The presence of antidepressants in study recruitment criteria will ensure additional safety if the trauma focused therapy triggered emotional distress which could temporarily activate depressive symptoms. The presence of antidepressants in all study participants will also ensure proper evaluation of the effect of propranolol without any confounders effect.
6. Agrees (if the participant is female and of childbearing potential) to use at least one of the following highly effective methods of contraception, such as hormonal contraceptives (e.g. combined oral contraceptives, patch, vaginal ring, injectables, and implants); intrauterine device (IUD) or intrauterine system (IUS); vasectomy and tubal ligation or alternatively double barrier method.
7. Agrees not to start any other therapy including self-help group during the trial period. Exception will be made for participants who had already started therapy and have been attending the sessions for at least 6 months.
8. Agrees not to start any anti-craving medications for alcohol use during the trial period. Exception will be made for participants who were already taking an anti-craving medication for at least 6 months.
9. Able to speak and read in English

Exclusion Criteria:

1. Diagnosed with a severe or unstable medical illness that precludes safe participation in the study as per study physician, including contraindications to propranolol administration such as asthma, diabetes, arrhythmia or congestive heart failure
2. Diagnosed with psychotic disorder or bipolar disorder
3. The use of alcohol abstinence medications within the past month
4. Current moderate or severe substance use disorder (excluding alcohol, cannabis, tobacco and caffeine)
5. A basal systolic blood pressure < 100 mm Hg or basal heart rate < 55 beats/minute
6. Pregnant or breastfeeding women
7. Individuals with known hypersensitivity to propranolol
8. Individuals with current use of medication that might interact adversely with propranolol such as anti-arrhythmic medication or calcium channel blockers
9. Current suicidality risk as indicated during the conduct of the Columbia Suicide Severity Rating Scale (C-SSRS) with concurrence after a study physician's evaluation if the response to C-SSRS questions 1 or 2 is "yes"28
10. Any participant known to have non-allergic bronchospasm such as chronic bronchitis, emphysema, bronchiectasis, hypotension, metabolic acidosis, severe peripheral arterial circulatory disturbance, untreated phaeochromocytoma, Prinzmetal's angina
11. Any participant with known hypersensitivity to any ingredient in the formulation, including any non-medicinal ingredient, or component of the container.
12. Any participant using catecholamine depletion drugs such as reserpine or guanethidine.